The Conservative MP said that as the Prime Minister looks to replace Mr Cummings, he needs to focus on delivering Brexit, coronavirus and recovery from the pandemic. Sir John insisted the three issues “have to be tackled together and are critically interlinked”.
Writing on his blog, Sir John said: “The first is the secure a clean exit from the EU, with or without the preferred free trade deal, with no more slippage.
“Indeed, there will not be a free trade deal of an acceptable kind unless the clear resolution of the UK to just leave is believed by the EU.
“The second is to put in place a full range of approaches to the virus as we await further breakthroughs from medical science, so we can live more normal lives and get the economy back to work whilst protecting the vulnerable and limiting the spread of the disease.
“I have often commented here on the initiatives we need to extend or develop to winnow down the impact of this virus.
“The third is to do everything we can to promote and sustain recovery.
“We need more and better-paid jobs, more and more profitable small businesses, more homegrown food and home-produced goods.”
Sir John also urged Mr Johnson to “build more bridges” with ministers and backbench MPs.
“He’s got a very talented, experienced team of technical experts around him.
“He’s led these negotiations from the start and obviously remains in place and continues to do so.
“So I don’t actually think the departure of Dominic Cummings makes any impact on the negotiations, since Lord Frost has been leading those.”
Negotiations between the two sides are going down to the wire this week and UK chief negotiator Lord Frost has warned a deal may not be struck.
He tweeted on Sunday: “Arriving once again in Brussels shortly for another round of negotiations with EU and Michel Barnier this afternoon.
“I and our British team have been in talks almost every day since 22 October.
“We are working to get a deal, but the only one that’s possible is one that is compatible with our sovereignty and takes back control of our laws, our trade, and our waters.
“That has been our consistent position from the start and I will not be changing it.
“There has been some progress in a positive direction in recent days.
“We also now largely have common draft treaty texts, though significant elements are of course not yet agreed.
“We will work to build on these and get an overall agreement if we can.
“But we may not succeed. Either way, as the Prime Minister Boris Johnson made clear on 16 October, people and businesses must prepare for the change that is coming on 31 December, most of which happens whether there is a deal or not.”