0441 GMT July 22, 2019
Ruth Davidson, the Conservatives' leader in Scotland, told party members that a cross-partisan agreement on Brexit was needed before this month's European elections, or Britain's major parties would face an even bigger backlash from voters, Reuters wrote.
The Conservatives lost 1,332 seats on English local councils that were up for re-election, and Labour – which would typically aim to gain hundreds of seats in a mid-term vote – instead lost 81.
Many voters expressed frustration at May's failure to have taken Britain out of the European Union, almost three years after the country decided to leave in a referendum.
"If we thought yesterday's results were a wake-up call, just wait for the European elections on the 23rd of May," Davidson told a party conference in Aberdeen.
Speaking to reporters afterward, she said there had been progress in the weeks of talks between the Conservatives and Labour to find a Brexit deal which passes parliamentary muster.
"There is a deal that could be done in the next few days ... and I really hope we can get to that point," she said, describing the results as "a kick up the backside".
Labour leader Jeremy Corbyn said on Friday there was now a huge impetus on every lawmaker to get a Brexit deal done.
But even if the Conservative and Labour Party leaderships reach a Brexit compromise, there is no guarantee that it will pass through parliament, which has roundly rejected May's proposals three times already.
In an indication of the hostility May faces from the most pro-Brexit wing of her party, former leader Iain Duncan Smith renewed his call for her to step down soon, calling her a "caretaker prime minister" after the local election losses.
Complicating the picture, the main beneficiaries of the swing against the two major UK parties were the pro-EU Liberal Democrats, who campaigned on a demand for a new referendum, aiming to reverse Brexit.
Health minister Matt Hancock urged pragmatism in a BBC radio interview earlier on Saturday.
"I think we need to be in the mood for compromise," he said.
Foreign minister Jeremy Hunt also saw a "glimmer of hope" that there might be a deal with Labour soon.