That would be London Bridge, but the one the song refers to was demolished back in the 19th century.
Royal mail post box.
Cup of tea.
Silhouette of Queen Elizabeth in profile - such as found on postage stamps.
Fish & chips
Flat cap & pearly king waistcoat
Nelsons Column
Mini car (especially witha union jack painted on the roof) and mini skirt
Oxford & Cambridge boat race
FA cup (soccer trophy)
HMS Victory
Don’t know why, but umbrellas always seem quintessentially British to me.
Or the hats that Andy Capp wears.
Deerstalker hat paired with a distinctive pipe?
Civil Servants? Then go for Sir Humphrey Appleby, Bernard Woolley, and Jim Hacker! (From Yes, Minister).
A Guardsman, such as guard Buckingham Palace.
A Spitfire.
I second an umbrella, but it should be rolled up.
The British Lion
Sherlock Holmes’s silhouette?
The song might refer to many things, but that isn’t one of them. London Bridge Is Falling Down - Wikipedia
I’m quite partial to Saint Paul’s, myself.
If it’s ‘British’ you’re after, maybe some non-London things? The Forth Road Rail Bridge? Edinburgh Castle?
A toast rack, not sure how to represent it in silhouette but it’s the ‘britishist’ thing I can think of.
A woman lying on her back and thinking of England.
A Rolls-Royce logo / grille/ The Spirit of Ecstasy
A Tube stop with “Mind The Gap” signs. Bangers and mash. The baggage retrieval system they’ve got at Heathrow (I’m so worried about it). Football hooligans. Rumpole with a glass of Chateau Thames Embankment. The Beatles. Twiggy in a miniskirt.
And it doesn’t look like anything. It just looks like an ordinary bridge.
An old-fashioned teapot seems like the most obvious thing to do a silhouette of. There’s nothing else that it could be confused with, and there’s no other place on Earth as associated with that style of drinking tea. (Russians and tea-drinking Asians have their own customs.)
Or if not that, how about a bobby helmet? Assuming the silhouette is black, you should be able to pull it off effectively. Putting a billy club nearby is optional.
A dowdy woman with an apron
The Anarchy symbol
A gentleman with a handlebar mustache, wearing a top hat, holding his cane in the air with a floating fish tied to it
You forgot bad teeth.
Well, if the ad campaign will be running in the UK, that’s different. Clearly my muddled tourist memories aren’t relevant. If the campaign were running outside the UK, that’s the level of recognition you’d get from foreigners, so your symbols could be less precise.
A 14-year-old smoking a cigarette and pushing a pram.
A curry house between an off-licence and a Pizza Hut.