Depends on the restaurant.
I've been to places were gratuity was explicitly included in the bill breakdown, and didn't leave an extra tip (unless the service was exceptional). And I've been to places where gratuity wasn't explicitly included in the bill breakdown, but the waitstaff were surprised when I did tip and alerted me (as an American tourist at the time) that it wasn't necessary. And I've been to places where they make it clear that no form of gratuity is included in the bill and to please remember to tip, and I've tipped then.
In the US, I usually tip a minimum of 20% after tax, but my fiance says that in the UK, only 10-15% is ever really needed. 20% in his opinion is a bit overkill, unless it's a favorite local and you have a good relationship with the staff there.