The vehicle swerved into a group of mainly North and West African people shortly after midnight as they left prayers at the Muslim Welfare House and the nearby Finsbury Park Mosque in north London, one of the biggest in Britain.
The driver, a 48-year-old white man, was grabbed at the scene by locals and pinned down until police arrived. He was arrested on suspicion of attempted murder.
After being seized, the man said he had wanted to kill "many Muslim people," one witness told journalists.
A man, who had earlier suffered a heart attack, died at the scene but it was not clear if his death was connected to the van attack.
The attack was the fourth since March in Britain and the third to involve a vehicle deliberately driven at pedestrians.
It came at a tumultuous time for the government with Britain starting complex divorce talks with the European Union and May negotiating with a small Northern Irish party to stay in power after losing her parliamentary majority in a snap election that backfired.