The entire country is out there, frantically packed into supermarkets, jamming up the car parks, tossing food and drink into their shopping trolleys. In this post, I want to suggest a few alternatives. As a Londoner, I can only speak for London shops, but I'd love readers to suggest other fantastic shops, in London and elsewhere in the UK in the comments. These are my picks, not just for Christmas but any time of the year.
My advice when visiting these shops is to make a day of it. Have lunch there or nearby. Take big shopping bags and fill them with new exciting bottles and jars, exotic cookware, strange fruits. Generally they are so cheap that if you don't like it, it's no big deal. Talk to the shop keepers, ask questions, hell I chat to the other customers, especially housewives who look like they have experience of cooking dinner for a large family for several decades. 
Italian:
Lina stores in Soho. Beautiful shop with pale green tiles, friendly knowledgeable service.
Clerkenwell used to be the Little Italy in London. Between 1880 and the First World War, hundreds of thousands of Italians moved here, including my great grandparents. My great grandfather worked for Carlo Gatti's icecream makers. (My parents still live in Clerkenwell.) The clown Grimaldi also lived in Clerkenwell and has a blue plaque. There is an annual Italian festival in the area, centred around the Italian church, with swaying processions and statues of the Virgin Mary. More Little Italy history here.
In Clerkenwell, I recommend the Italian shop Gazzano's, known for Puglia bread.
Also the vintage Continental Stores down the road in Kings Cross. Run by an elderly couple, they don't have a great deal of stock by modern day standards, but it's worth visiting just for the shop front.
Online Italian shopping:
Try this new company. Delicatezza, they sell fresh UK made burrata and unusual stripey tortellini.
Food Halls:
Fortnum and Mason. Piccadilly.
It's 300 years old, started by a royal footman from a spare room in his house, it eventually expanded into the most beautiful food shop, possibly in the world. It is not as expensive as you'd think. I once bought some heritage potatoes at Borough market, then discovered they were cheaper at Fortnums. It's a pleasure to enter this old fashioned food hall, with exquisitely packaged products, many own brand, and frock coated shop assistants. There is nowhere else like it. Interestingly, they employ a historian on site.
Selfridges, Oxford st:
It has become more adventurous, food-wise, over the last decade, bringing in people like Bompas and Parr to do food and drink installations on the roof, commissioning stunning foodie window displays and housing boutique restaurants. And of course, a fantastic selection of some of the most interesting food products from all over the world. A good selection of American products.
Markets:
Broadway market, Saturdays, London Fields
I feel very envious of those living in Hackney having access to this now trendy but authentic street market. It's actually quite recent, in the last five years, that it's become a place to go. When I was squatting in London Fields pool in 2002-5, there wasn't much happening yet. Cheaper than Borough and less corporate, it is the testing ground of many a famed street food producer including banhmi sandwiches, artisanally smoked salmon, Violet cakes to name but a few.
Borough Market, London Bridge
This was the first revival of the artisanal food markets, but a victim of it's success, and far too touristy on Fridays and Saturdays. Best go on a Thursday. Still got Neal's Yard Dairy though, the best place for British cheeses, selling also Irish tea and Maggie Beer's verjuice. Go early to Neal's Yard, the queues at this time of year are horrendous.
Portobello Road Market, Ladbroke grove tube.
Mixed among the tourists and the Notting Hill set, this market remains a true working class street market, with hard as nails women (fake tans, plucked eyebrows, backcombed hair, under their quilted jackets but these ladies are impervious to all weathers) shouting out bargains in authentic cockney. A wonderful mushroom man at the end, good fresh produce, some cheap deals to be had on cheese and chocolates.
Ridley Road Market: Dalston junction.
Turkish, Jewish and Caribbean foods, very cheap, a good bagel shop and a large branch of PartyParty.
Brixton Market:
Not just the market but also the arcades of hip Brixton village, a jumble of inexpensive exotic foreign produce, 'jungle' meat, fresh produce and tiny (in size and menu) restaurants on their first stepping stone from supper club or street food stall to high street domination. It's the other end of London for me, so I rarely go but well worth a visit.
Asian food:
Wing Yip, Cricklewood.
This family run emporium started in Manchester and has a large branch in Cricklewood, near Staples Corner. Hence it's only, realistically, reachable by car but they do also have online shopping. On Sundays this place is buzzing, with food tastings and a crowded restaurant. The prices are fantastically cheap and the staff are helpful. They even pack your bags for you. There is a wholesale section at the back, useful for buying in bulk. They also sell some Chinese cookware and tableware. The whole place smells faintly of Durian fruit, but sweetly not in a stinky-feet way. I love coming here, it's an interesting trip in itself as you'll discover new foods.
Chinatown:
There is a whole street of Chinese supermarkets. You find some weird stuff there. I wish they had food demonstrations and more English language explanations of some of the stranger products like the little black nuts (?) that look like vampires.
Mare Street:
After visiting Broadway market, you could graze around the Vietnamese supermarkets such as the Le Mi Supermarket and Video Store on Mare St.
Japan Centre, Shaftesbury Avenue:
Bloody expensive but intriguing with great quality sushi which you can eat in or takeaway. Excellent vegetable peelers for sale and loose leaf Japanese tea.
Natural Natural, Finchley Rd and Ealing Common
I go to this Japanese shop as it's near me. The staff are very sweet and helpful, they have a cartoony notice saying 'How do you eat these things? We are always happy to help you, from the natural natural staff'. On the fruit and veg stall outside, you can buy fresh burdock and lotus root plus everything is very carefully wrapped as if it were precious, even single carrots. In the chiller there is a large selection of fresh tofu in different textures from super silky to extra firm.
Middle Eastern food:
Persepolis, Peckham
You will most likely be served by a flame haired woman, a cookbook author named Sally Butcher. I spent a day there helping out, which was great fun. Sally will happily talk about the food they sell and can speak fluent Persian. People travel from all over the UK and Europe to buy their authentic imported Iranian foods, especially the flown-in pastries. A little counter, selling some of Sally's food, is in the back.
Edgware road:
Plenty of fascinating food shops, all very good value, in this area which has become London's Little Arabia. Green Valley supermarket is one good name that is bandied about. Afterwards you can dip into one of the cafés, have a mint tea or strong silty coffee and smoke a fruit tobacco hookah.
Indian:
V and B supermarket (Wembley and Southall)
I can spend hours here, photographing and taking notes: the sugar loaves, the open vats of pickle, the fresh spices. This whole area is worth a half day of your time: enamel bowls, bargain large saucepans for bulk cooking, chaat stalls, fresh 'tinda' (Indian pumpkins), dirt cheap buckets of creamy yoghurt, green curry leaves, thin wooden chapati rolling pins. You feel like you have travelled to India. Heaven.
Eastern European/Kurdish:
Where2save 352-354 Kilburn High Rd and Harlesden.
We used to have Food World in Kilburn, a treasure trove of unusual foods from around the world, crammed into one shabby supermarket. The landlord wanted to triple the rent so this local resource disappeared. Never mind! We now have Where2save a few doors up. Run by kurds, this small shop is expanding every year. The range of their products, compared to a conventional supermarket, is impressive. How do you compete with the supermarkets? I asked the owner. By making sure that we stock different products to the big four, he replied. Their fruit and veg stall outside has fresh, good quality produce that puts supermarkets to shame. Every time I visit, I try a new Eastern European dairy product, or Brazilian tempera or one of the huge selection of inexpensive nuts. If I want a chowchow, some Georgian-style green plums, Turkish 'sultana' grapes, chervil, some tiny Indian limes for pickling, sour cherry fruit leather, this is where I go.
Grocers:
Newington Green, Newington Green, Islington.
Not only do they have super fresh, unusual fruit and veg, they use any spoiled or leftover fruit to make their own jams, chutneys and pickles. Extremely helpful staff who will carry to your car. An emotional paen to this shop is written by my fellow blogger Rocket & Squash.
Clifton Greens, owned by the same people by in Maida Vale. I bought some great food there, such as preserved mandarins in jars and fresh jalapeño peppers.
Andreas Veg in Chelsea, probably the best quality fruit and vegetables in London.
Caribbean food:
Blue Mountain Peak, Harlesden:
My Caribbean friends make the journey to this shop in murder mile in Harlesden to get authentic products. They've just gone online too, so everyone can order from them.
Hackney, Dalston and Brixton are also good areas for Caribbean food.
Comments appreciated...thanks