The Conservative peer, who has led negotiations with the EU, quit the Government with immediate effect over the weekend after his initial plan to resign in January – agreed with the Prime Minister – became public.
In his resignation letter, the former Brexit minister cited “the current direction of travel” of the Government, as well as fears over “coercive” Covid measures and the wish for the UK to become a “lightly regulated, low-tax” economy.
Foreign Secretary Liz Truss has taken over responsibility for the UK’s future relationship with the EU.
Speaking for the first time since his departure, Lord Frost expressed his “huge admiration” for what Mr Johnson has done as a leader in ensuring the UK exited the EU.
He told Sky News: “We have never disagreed in any way about Brexit policy.
“Right up to the last day we’ve been absolutely aligned on that, and Liz Truss and Chris Heaton-Harris, I’m sure are going to do a great job.
“I left the Government because, as I think is well known, I couldn’t support certain policies – most recently on Covid restrictions and Plan B.
If you’re a minister you have to support collective responsibility, you have to support decisions of the Government, and I couldn’t, so that’s why I had to leave
“And if you’re a minister you have to support collective responsibility, you have to support decisions of the Government, and I couldn’t, so that’s why I had to leave.”
Lord Frost said his resignation was “absolutely not about leadership”, adding: “I’m absolutely confident this country has a great future under Boris Johnson’s leadership if we can get the policies right.”
Asked if Mr Johnson is the right man to carry on as Prime Minister, Lord Frost said: “The departure is about policy differences, and I’m absolutely confident that he’s the right man to take the country forward.”
On whether more ministers will resign if Mr Johnson implements further Covid restrictions, Lord Frost said: “I can’t speak for anybody else, I can only say what I think, which is that I don’t support coercive policies on Covid.
“The Prime Minister has got some very difficult decisions to take and I’m sure he’ll be thinking very hard at them.”
Downing Street said Ms Truss would take over ministerial responsibility for the UK-EU relationship, and would lead negotiations to resolve issues with the Northern Ireland Protocol.
Ms Truss underwent a transformation from being pro-Remain to an avid Brexiteer following the referendum in 2016.
DUP leader Sir Jeffrey Donaldson said he felt Lord Frost believed the time was “fast approaching” when the UK Government needed to act unilaterally over the Northern Ireland Protocol.
Sir Jeffrey told the BBC: “I have to say from the conversations I had with Lord Frost, he was concerned that there is still a very substantial gap between the EU and the UK in the negotiations.
“He felt, I think, that we were fast approaching the time when the UK Government needed to take unilateral action.
“I do think that it harms the Government’s position when you lose your chief negotiator in these circumstances and I think that the Prime Minister needs to get to grips with this issue.
“He needs to recognise this is a priority issue, alongside the other priority issues, that he is dealing with at the moment.
“Whilst I welcome the appointment of a senior cabinet minister, Liz Truss, to take on the role of chief negotiator, we need to see a much sharper focus now on getting this sorted out.”
Sir Jeffrey said it was now time for the Prime Minister to act unilaterally over the Northern Ireland Protocol.
The Prime Minister’s official spokesman, asked about Sir Jeffrey’s call for action in the new year, told reporters: “I’m not going to speculate on Article 16 beyond saying we still believe that the boundaries for triggering Article 16 have been met, but our preference is to continue the discussions we’ve had with our EU counterparts.”
On why there is no Brexit minister now in the Cabinet, he replied: “We will have the Foreign Secretary who takes on those responsibilities in Cabinet as you’d expect.”