Nyki mentioned one, but other number ones while this was on were:
19th April - Desmond Dekker and The Aces: The Israelites
26th April to 31st May - The Beatles with Billy Preston: Get Back
7th June - Tommy Roe: Dizzy
And of all four I have only ever heard(of) one of them and that's Dizzy.
The Israelites was the first ever cross-over reggae hit in Britain, and one of the best. And the Beatles - well, were the Beatles. Get Back was the one they did on the roof of the Apple building, which was their last ever live performance.