Punctuation is mostly universal; a few habits are distinctly British.

Quotation marks: British publishing favours 'single quotes' first, doubles inside: 'He shouted "wait" and ran,' she said. (American style reverses this.)
Logical punctuation: commas and full stops go outside the closing quote unless they belong to the quoted words: She called it 'a triumph'. vs She asked, 'Is it over?'
Abbreviations: no full stop when the last letter survives: Mr, Mrs, Dr, St, Ltd — but Prof., etc., e.g. keep theirs.
The Oxford comma (before final and) is optional in Britain — use it only to prevent ambiguity: I thanked my parents, the Queen and God vs …my parents, the Queen, and God.
Semicolon joins two full sentences (The train was late; the platform was packed); colon introduces an expansion or list.
Apostrophes: plural + ' (the teachers' room); irregular plural + 's (children's); never for simple plurals: ✗ potato's £1 — the infamous greengrocer's apostrophe.
Dates & floors: British dates run day–month–year (6 August 2026); the ground floor is below the first floor.