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For usual stuff, just go to Harrod's in Knightsbridge and be done with it.

For real foodstuffs though start here...

Vacuum pack at Neil's Yard Dairy.

http://www.nealsyarddairy.co.uk/ourshops.html

If you're into game (and game is very good in Europe), try Rules if you want very traditional or my fave St. John (run by Mr. Head to Tail himself).

http://www.stjohnrestaurant.co.uk/

I may post more later if I have time. Cheers and have fun.

(I'm in London myself Monday/Tuesday.)

for indian/curry/kebab -- avoid brick lane, and head a little further east to a place called new tayyab. (http://www.tayyabs.co.uk) amazing lamb kebabs, fairly inexpensive, almost always a wait .... but completely worth it. (note -- it's byob.)

Agree with Kathryn! Buy all the chocolates (mmmm Cadbury) with funny names that you can't find much of in the States. Entertain your friends!
Also, shortbread. Walker's with the red plaid box is classic.

fortnum and mason. one-stop shopping.
you can get a great range of biscuits at heathrow actually.
i recommend the cocolate coated bath oliver biscuits. hard to find, but worth the hunt. also prince charles' duchy of cornwall line is very good as well. i like the orange, the ginger and the oaten. theres a great foor market under the london bridge statio, particularly on saturday.

Hi jperlow, I live in London and have loads of ideas, but before I suggest anything I'm just wondering what neighbourhood you'll be staying in and how much time you'll have to shop around? Only, London is a massive city with slow public transport. So a bit more info would help.
Cheers.

Flake bars. Break them up over ice cream mmmmmm. Breakfast tea. All kinds of chocky and biscuits. Odd crisps (odd for here) Shrimp and chili, any kind and chili. spotted dick in a tin. (no really) Lyles syrup the recipe for wings on the jar is not too bad.

For a must-see food market, I'd recommend Burrough Market, which is right next to London Bridge (Southwark Cathedral). It's open on Fridays and Saturdays.
For a fish and chip place, I like North Sea Fish Restaurant, in Leigh Street off Russel Sq. I think there are some good ones in the Notting Hill area as well, but as an East End girl, I never go there.
I agree about avoiding brick lane curry (I actually live on brick lane, and we never eat in any of them). Tayyab is great. If you're in the East End, go to G. Kelly, a pie shop in Bethnal Green Road for a true London experience, or go to E Pelicci, a traditional caff that still has the original twenties art deco-but-working-class decor.
If you are going into the East End, The Golden Heart might be a fun pub to go to. It is the notorious hangout of loads of well-known young British artists (Tracy Emin, the Chapman brothers, etc.). It's actually a really good pub, though. I also love the Approach in Bethnal Green. For something more ye olde Englandish, the Seven Starts, which is directly behind the Royal Courts of Justice, might be a good bet. It dates back to 14somethingorother and it's really an amazing little space with lovely food as well. Many regard it as London's best pub. And sometimes when you're there you get a glimpse of a law lord dashing down the street in his gown.
It's hard to recommend a curry restaurant, because there are so many. My favourite is Rasa in Stoke Newington (the original one - some of the other branches are crap), which does Keralan food that is truly a revelation (I think I waxed poetic about their beetroot curry in another post). Sagar in Hammersmith is also good, but then, I love South Indian cuisine. For more high-end places (and meat) in Central London I like the Red Fort in Dean Street. Tamarind, in Queen Street, Mayfair, was also great when I went there.
For kebabs, my boyfriend recommends 19 Numara Bos Cirrik, an ocakbasi in Dalston (Stoke Newington Road). The grilled meat is apparently amazing, including fantastic grilled quail. For Turkish, I love Sariyer Balik, an unpreposessing place in Newington Green that does wonderful, very fresh, grilled fish. Yum.
I'm not sure about British food to take back, since I'm not sure what there is in the States. I have to admit I'm pretty taken aback by the collective fascination with Walkers, and also by the idea of dragging back a Heinz-brand spotted dick in a tin (they do a treacle sponge one that I like better, if you're into that sort of thing). I recommend branston pickle and piccalilli. Hob Nobs - do they have then in the States? They're chocolate covered oat biscuits and they're delicious. Get them.
I know it's cliche, but I'd visit Harrod's food hall. It's such a spectacle.
I'll probably think up some more, but that's it for now.

And, sorry, that should be The Seven Stars.

Oh dear, I'm sorry that post was so long.

caley, telling us about tasty things is something you never have to apologize for!

That's probably true. There is, however, a class of British snack food that I suspect is too trashy to export. Hulahoops and Wotsits, for example - I guess they're the British answer to Cheetos. I have a soft spot for ham and pickle flavour crisps, which are not made by Walkers, but by some slightly trashier company.
I would definitly go to Burrough Market, as there's quite a lot of extraordinary food there, including some very unusual regional things.

Also, out of curiosity, has anyone had samphire? It's not really the season for it now, but that's something I think I've only ever seen in Britain.

Aah, forget Harrods! Fortnum & Mason, all the way. The grocery is smaller than Harrods, but the prices are not *as* bad and it's all quality stuff. The tea selection alone is amazing. Also, if you have time for a tea, they do a wonderful one. I brought home tea, lemon curd and mustard from F&M.

Also, I agree with the above posters, go to a Boots or Tesco and wander around the candy/junk food aisles. The Hulahoops are delicious and the Galaxy bar with hazlenuts is my favorite chocolate. Ever. Plus, the Brits have tons of interesting flavor combos on their "crisps."

I was in Ireland over Christmas, and I brought home ploughman's sauce (kind of like a chow-chow, or chutney if you're not from PA), HP sauce, and LOTS of McVitie's (a "digestive" biscuit with a plain chocolate coating). McVitie's are delicious with tea.

By the way, I did end up with some Fortnum and Mason stuff as well, but from the Duty Free shop at Heathrow.