Scottish Tory leader Ruth Davidson has conceded there is “scepticism” about Boris Johnson becoming the UK’s next prime minister – but has vowed she will judge him on his actions.

However, the Conservative MSP said the incoming PM “needs to deliver”, and that he only had a “very small window” of time to finalise Brexit.

Ms Davidson said she had been a critic of the former foreign secretary when she thought he had “merited it”, and vowed to continue with this stance.

But she told BBC Scotland: “He’s prime minister, he’s won it fair and square, and most fair-minded Scots across the country will judge his premiership by his actions in office, as I will.”

In the contest to succeed Theresa May as PM, the Scottish Conservative leader first backed Sajid Javid – who she described as “head and shoulders above the rest” – before supporting Michael Gove and then Jeremy Hunt.

After Mr Johnson was elected as the new Conservative leader, Ms Davidson said: “I’ve been perfectly open and honest with him, and with the country – he wasn’t my choice for leader, I didn’t vote for him.

“However, I will judge his premiership by his actions in office, as will everybody across the country, whether they are parliamentary colleagues, whether they are voters, whether they are opponents.”

She added: “There is no job like prime minister, there is nothing that can prepare you for it. I’ve been lucky enough to see it up close. We will see what he makes of it, and he is going to have to make a pretty good fist of it pretty early, because of the challenges he is facing that previous prime ministers haven’t faced.”

Mr Johnson now faces the “enormous task” of delivering Brexit, with Ms Davidson saying: “In terms of his inbox he’s not got his troubles to seek. I think first at the top of everybody’s is making sure he can get a Brexit deal across the line.

“He’s got a very small window to do that. I hope he can, I hope he can come back from Europe with a deal on the table.”

Boris Johnson has been elected as the new leader of the Conservative Party and the UK’s next prime minister (Victoria Jones/PA)

She revealed that during the leadership race she had had “several” conversations with Mr Johnson “to make sure that he can respond to concerns about him”.

Meawnhile Scottish Tory MPs met the former foreign secretary last week to discuss their priorities for his premiership, with these including a “Union Unit” within the Government and backing for key Scottish industries.

Ms Davidson said: “I think he needs to deliver, and I think there is a scepticism, not just in Scotland but across the whole country, about what kind of prime minister Boris Johnson will be.

“We will only know that once he is in office, but warm words aren’t going to be enough, we need to see some actions.”

She also urged Mr Johnson to keep David Mundell as Scottish Secretary when he appoints his cabinet – despite Mr Mundell having previously said he would find it “extremely difficult” to serve under Mr Johnson.

Ms Davidson said: “I think the new prime minister would do well to take his (Mr Mundell’s) advice on Scotland. He knows the Scottish Government inside out, he has sat across the table from Nicola Sturgeon and looked her in the eye many times, and I think that experience will be invaluable to the new prime minister.”