Actually, I think a good way to write British dialogue is to use British spellings. Colour, centre, criticise, favour, that makes even generic text subtly different from say any Americans in the page
also I would avoid using too much slang. there is a risk of it coming across like Dick Van Dykes 'cockney' accent. Instead i would use English word for american things like:
elevator = lift
Zucchini = courgette
eggplant = aubergine
sidewalk = pavement
freeway = motorway
also there are some very subtle things you can do depending on where the story is set. for example. if your story is set in central Europe, people will be driving left hand drive cars, and in the past i called shotgun and ended up in the driving seat of someones car
also how we cross the road will be different to you. in England we would look to the right first when crossing the road or joining traffic. imagine doing that in a country where they drive on the right and not seeing anything, you would think it was safe to step out without really checking to the left meaning you end up stepping out in front of a car
also , yes loo, quid and bloody are really well known slang , but day to day, i barely use or hear them
beware the 'posh London accent'. what you are describing could be 'received pronunciation' which was a accent adopted by actors and tv presenters in the 1950s to the late 1980s it started fizzling out with the kitchen sink dramas of the 60s and by the late 80s the trend for people to use their own accents became the norm.