The party enjoyed success across the United Kingdom and by early morning had gained more councillors than all the other parties combined, according to Sir Vince.
It won two key councils in south-west London, building on gains in last year's general election in Richmond and Kingston.
51 seats were up for grabs at SLDC, which has been under Liberal Democrat control for the last 12 years. A year later, the parliamentary party faced near wipe-out.
But for the Lib Dems it was a more straightforward success.
Polling expert Professor Sir John Curtice said his analysis indicated the Lib Dems were up three per cent since most of the English seats were last contested in 2014. "The Government have very clearly taken their eye off the ball".
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Major casualties include deputy leader David Lee who was ousted from his Norreys ward seat by Labour candidate Rachel Burgess.
With just one of the 150 results awaited, Labor had gained an extra 59 councilors, taking their total in England to 2310.
The Liberal Democrats have snatched a flagship Conservative council in South Cambridgeshire which did have a Tory majority of 15.
Cable said the party had shown "we can win anywhere", pointing at wins in Liverpool, Sunderland and Gosport, "in both leave and remain areas".
Group leader Martin Goss said: "We shall be discussing what happens next among ourselves over the weekend and with other parties over the next two weeks - we are not making any immediate decisions but will talking about how to move forward".