By Sam Francis & Paul Seddon
Political reporters, BBC News
The Liberal Democrats have won 104 new council seats and gained control of two councils in Thursday's local elections.
Lib Dems now run Dorset and Tunbridge Wells councils, but failed to take one of its other key target of Wokingham.
The party made gains in traditionally Conservative voting areas of the south of England, known as the "blue wall".
Leader Sir Ed Davey claimed voters were switching from the Tories because they "have had enough of being taken for granted and being let down".
The Lib Dems won extra council seats in West Oxfordshire, Winchester and Cheltenham, while gaining control of Dorset Council from the Conservatives.
With just one of 107 councils to declare, the party has returned 521 councillors at these elections, more than the Conservatives on 513.
This would be the first time since 1996 it has beaten the Tories in a local vote, although historical comparisons between local elections are tough because of the different seats up for grabs each time.
On Saturday, the party took the London Assembly seat for the South West constituency, which includes the boroughs of Hounslow, Richmond and Kingston.
The BBC's projected national share, calculated using results from key wards, has the Lib Dems on 17% nationally, behind the Tories on 25%.
This is down three points on last year - when the party hit 20% for the first time since entering into coalition with the Conservatives in 2010.
But it is broadly in line with its projected share since the Brexit referendum in 2016.
Sir Ed said Conservative MPs would be "looking over their shoulder" ahead of the general election later this year.
To emphasise the point at a rally on Friday, party activists wore inflatable dinosaur costumes and blue Conservative rosettes holding a banner saying "Make this Conservative government history".
Under Sir Ed, the party has become well known for campaign stunts featuring large and outlandish props.
These have included turning the hands on a clock face in the style of Parliament's Big Ben, to demonstrate "time's up" for Rishi Sunak, and Sir Ed knocking down a giant blue wall with an orange Lib Dem hammer.