Liberal Democrat leader Sir Vince Cable says his party is "beginning the fightback" after gaining dozens of seats in the English local elections.

"We are reasserting ourselves as a major national force," he told supporters in Richmond in London, where the party won control from the Tories.

It also gained Richmond's neighbour Kingston, South Cambridgeshire and Three Rivers in Hertfordshire.

Sir Vince claimed the party's critics were being proved "completely wrong".

It marks an improvement from the party's poor showing the last time the seats were contested in 2014.

Across the 150 council elections the Lib Dems increased their tally of seats by 75, the most gains of any party, and kept control of five councils.

Based on the results, the BBC's projected national vote share puts the Lib Dems on 16% - an improvement on the latter days of the coalition government between 2013 and 2015, but lower than its estimated performance in last year's county council elections.

BBC polling expert Professor Sir John Curtice added: "It is thus far from clear that the party has secured a marked revival in its overall performance this year, and its projected share is certainly well down on the 25% or so of the vote that was routine for the party in local elections held before the formation of the coalition in 2010."

Sir Vince also pointed to gained seats in Hull, Sunderland and Liverpool, claiming the pro-EU party was winning ground in both Leave and Remain-backing areas.

The Liberal Democrats have put a pledge of a referendum on the UK's final deal with the EU at the heart of their pitch to voters, hoping to gain Remain supporters alienated by the two largest parties' stance on Brexit.

But they have yet to recover the electoral ground lost after they joined the Conservatives in coalition government between 2010 and 2015.

"These things don't happen overnight," Sir Vince said.

"But I am absolutely certain that those people who wrote us off are now being proved to be completely wrong."

Polling expert Professor Sir John Curtice said the party had seen a sharper increase in vote share in areas with a large graduate population, saying it may be having "a measure of success" in reconnecting with that market.

Lib Dem home affairs spokesman Sir Ed Davey, whose wife was re-elected as a Kingston councillor, said it was a "great night" and a "sign of things to come".

He told BBC Radio 4's Today programme voters were "desperate" for a party that was neither "right wing Brexit Tory" or "left wing Corbynista".