Residents living in 88 local authorities across England, Scotland and Wales took to the polls on Thursday, with results declared on Friday indicating a boost for Theresa May ahead of next month's General Election.
Christian and former-Conservative MP Sir Gerald Howarth told Premier the Tories were keen not to become complacent following the gains.
He said: "I know the party's very keen to play down expectations, that we're taking nothing for granted. Some people have said that this general election will be a coronation. It's nothing of the sort."
Among their successes, the Tories were victorious in Harlow and Lincolnshire, while they also became the biggest party in Cumbria.
With their voters turning to the Conservatives, Ukip suffered significant losses.
Spokesman for Christian on the Left (which supports Labour), Stephen Beer told Premier why he felt it had been a "tough night" for the party.
Explaining why, he said: "These are local elections and in some areas there are particular local issues which are in people's minds and that has affected votes for certain councils.
"Secondly, I think we have to remember that we did win a fair number of seats four years ago... we had a head wind."
The Liberal Democrats experience mixed results, failing to breakthrough against the Conservatives in the south west of England but they saw a particularly marked boost in Hampshire.
Lib Dem former business secretary Sir Vince Cable said: "We're in a relatively encouraging position, though there hasn't been a spectacular breakthrough."
Former Ukip leadership contender Lisa Duffy told the BBC: "As a party we will learn from this, we will grow and we will move forward and we will continue to be positive."