Straight answer

How much validity do I need on my passport?

For Europe, on the day you travel your passport must be less than ten years old, and it must have at least three months left on the day you leave. Many other countries, including much of Asia and the Middle East, want six months' validity, so treat six months as the safe rule of thumb worldwide. Check the entry requirements page for your destination on gov.uk, and if renewal is close, do it before you book flights: names on tickets must match the passport you travel on.