Not sure the Bagel Bake on Brick Lane counts as street food, except that you'll end up eating your filled bagel on the street - you should try both the salt beef and chopped herring. If you go on a Sunday, round the corner Spitalfields Market has a good selection of different street style foods.
If you're in the City on a weekday, there's a stand right next to St Mary Aldermary (Bow Lane & Cannon St) with an weird-but-good mix of Peruvian food (arepas, etc.), healthy-Med salads, organic snacks, and fresh juices.
A short walk away is Leadenhall Market, a beautifully-restored Victorian dining/shopping arcade with some good food vendors (particularly the dried fruit folks). Don't go on a weekend, though ... it's completely dead then.
[On edit: it's the fruit that's dried, not the folks. Just in case anyone was unclear on that. :) ]
You will not find NYC-type street vendors in the UK (nor, generally speaking, anywhere in Europe). It's not something we have ever got into having.
As others advise, avoid the hotdog/burger carts you might come across near tourist attractions. At best they are awful and, at worst, pose a serious health hazard (an area where our food health & safety legislation and enforcement badly lets us down)
Check out this link discussing the question of street food in London
http://www.dimsum.co.uk/food/londons-... - La creperie is a perennial favourite, being in my part of town.
I would also recommend Whitecross Street market (off Old Street) which is a weekday market with stallholders selling various items. There are a few food carts and vans offering decent Caribbean, Thai and Indian fare. The standout for me is an Indian brother and sister team who make a very tasty samosa chat and offer a daily selection of home made vegetarian curries. To identify them, look out for their t-shirts featuring caricatures of the brother and sister.
Avoid the hotdog/burger carts at all costs, their "food" is vile.
alexjames is right. You will not bump into any breakfast carts like you do in Manhattan... nor is a cheap and cheerful hotdog available. It is becuase of England's favourite issue "health and safety" (a load of old rubbish if you ask me).
What I can recommend is going to Borough market on a Friday if you can (Saturday is very busy). There's all sorts of nice foods from wild boar sausages, to falafal, to scallops and noodle dishes available fom the stands at the market.
Best thing I can suggest as far as 'street food' goes.
No useful street vendors will be found in London.
It sure aint like NYC where I gather you can eat well on the streets.
Problem is, I think, food safety legislation along with the UK legal concept that you are not normally allowed to obstruct the highway. A highway includes the sidewalk.
There are a few exceptions. Ice cream vans are to be found but the product on sale will be of low quality. Vans selling revolting burgers etc are to be found outside sports venues. They are for the foolhardy only.