Sadiq Khan has warned progressive voters that they risk handing the London mayoralty to an “increasingly rightwing” Tory party unless they back Labour, amid concern in his camp that most Londoners are unaware of a complete overhaul of the voting system.

The battle for control of City Hall next May will be the first mayoral contest to switch to the first past the post voting system. It comes after a legal change last year that appears to be largely unknown among the capital’s voters. The previous system allowed voters to pick their second preference.

Only 30% of Londoners are aware of the change, according to a new Opinium poll. It has led to concern in Khan’s team that, despite his large poll lead, Liberal Democrat and Green voters will be unaware that they can no longer back him as their second preference, as many have done in the past.