This is an experience answer, no links from me here.
As a regular visitor to the UK and going out with locals, I have seen both.
In a busy pub, most people do not leave money on the table as the staff can miss it being there.
But when the pub is quiet, like after the end of the lunch rush, it is quite common to see people leaving money on the table.
Photo by Willeke
When you pay for food or drinks, you can just add money to the bill and pay more or round it up and tell the staff that they can keep (part of) the change.
If you are just buying drinks, or pay for the drinks separate from paying for the dinner, you can again add to the money to be paid, but I have heard quite a few English people say: "and one for yourself" meaning that the bar man can take a drink on your cost but often they just add a drink to the bill but put the money into a tips piggy bank.