At restaurants in London, many will add the equivalent of 10-12% onto the bill as either service or gratuity..so no need to tip.
In a Pub, if you have to go up to the bar to order food and drinks, no tipping.
In a restaurant, or a pub, if you are seated at a table and a server takes your order, and there is no service charge on the bill, then tip along the lines of 10%
Outside of London and the very most Tourist type places, assume tipping is a non-issue.
Not many places add the service charge to the bill but it is becoming more and more common, particularly amongst chains so it's always advisable to check the bill. This is by no means confined to London, it's nationwide so whilst tipping in general isn't much of a tradition in the UK it is becoming more and more expected in restaurants or pubs where table service is provided, not just in London but everywhere and the common amount is %10. But again, don't feel obliged if you weren't satisfied with the food or service.
And yes, just as nobody in the US tips a McDonalds or Wendy's server there's no reason to tip bar staff in a pub if you're ordering food or drink at the bar. Quite often regulars at a pub may offer to buy a member of staff a drink when they hand over their payment at the end of the night, this isn't explicitly meant to mean that they're going to pull themselves a drink there and then but they'll take the equivalent amount from your change and keep it.