Tory MP Mr Rees-Mogg is expected to attend rallies held by the Leave Means Leave group alongside ex-Brexit Secretary David Davis.
Former Ukip leader Nigel Farage and Labour’s Kate Hoey are also supporting the campaign urging Mrs May to axe her Chequers plan.
The group has also taken out adverts in 30 regional newspapers dismissing Ms May’s blueprint as the “same old, same old”.
A series of rallies will begin in Bolton on Saturday followed by Birmingham, Torquay, Bournemouth, Gateshead and Harrogate.
Richard Tice, Leave Means Leave vice-chairman, said: “We have relaunched the Leave campaign and we will stop at nothing to ensure the Prime Minister chucks Chequers and delivers Brexit in its entirety.
“Leave Means Leave will be engaging with as many people across the country to ensure Project Fear is torn apart so that the economic benefits of are revealed.”
Meanwhile, London mayor Sadiq Khan claimed British police already preparing for “civil unrest” after Brexit.
Mr Khan said: “Let me tell you the facts, which are that the police currently are preparing for the possibility of civil unrest. That’s happening now, already.”
Urging the Government to hold a second referendum, he added that Brexit was already having an impact on “understaffed NHS wards”.
See below for our rolling coverage of Brexit news throughout the day…
4pm: A future PM could change the UK’s relationship with the EU says Michael Gove
Speaking on the BBC’s Andrew Marr show, Mr Gove said: “A future prime minister could always choose to alter the relationship between Britain and the European Union.”
Mr Gove said that Theresa May’s Chequers plan was the right one “for now”.
3:30pm update: Brexit minister Chris Heaton-Harris said Brexit WILL result in the Government spending more elsewhere
Speaking on the BBC, Mr Heaton-Harris said: “When we stop paying the – I can’t remember the net sum that we are paying to the European Union this year but I think it’s about £11 billion – huge amounts of money into the multi-annual financial framework of the European Commission’s budget in a couple of years’ time – yes, there will be more money for us, the Government, to spend elsewhere.”
Latest figures from the Office of National Statists reported the UK’s gross contribution to the EU budget consisted of £19 billion before the £5 billion rebate was applied.
2:30pm update: Ex-Europe minister predicts Brexit talks lasting ‘Brexiternity’
Former Europe minister Denis MacShane has predicted that without a second referendum Brexit negotiations will dominate the UK for the “next ten years” in a shock prediction of “Brexiternity”.
He told LBC this morning: “Brexit has become a plural. There are several different types of Brexit.
“I don’t believe the House of Commons will want to vote for a full-on amputation.
“That will see no more commerce, no more flights taking off, no more easy driving or living in Europe. Some kind of fudge will be found.”
2pm update: Research shows that UK savers are not concerned about the impact of Brexit
A financial investment expert has said that Britons are committed to saving cash in currents accounts, regardless of the outcome of Brexit.
New research, conducted by financial analysts, has found that while big business and governments are impatiently becoming jittery in light of their future, the average Briton remains unmoved by the outcome of the UK’s exit from the EU.
The survey was conducted in August for BondMason by market research agency DRG, who interviewed more than 1,000 UK adults holding more than £25,000 of savings or investments.
The report stated: “A key finding was that only a small percentage of investors were worried by siren warnings over Brexit, but many remain stuck in a malaise over where to keep their money.”
12.45pm update: Gove hits out at EU but refutes support for Hungary
Mr Gove said it was “not true” the Conservatives supported controversial right-wing Hungarian leader Viktor Orban, who critics claim is anti-democratic and anti-Semitic, but said Brussels should still not interfere with individual member states.
Tory MEPs opposed measures in the European Parliament to censure Hungary, he said.
Mr Gove told BBC One’s The Andrew Marr Show: “It’s a long-standing principle of a number of MEPs from different countries and from different parties not to believe that the European Parliament should interfere in or censure the internal democracy of a particular country.”
Asked if the party had declined to vote against him because it needed his support, Mr Gove replied: “No, because I think it would be wrong for me at a time when we need solidarity against a number of different threats, you mention anti-Semitism, we need to make sure that our voice is clear, our position on these issues is absolutely clear and resonant and I don’t believe that individual criticisms of the kind you are understandably attempting me to make necessarily help us in ensuring we get both solidarity on the issues that count and the best deal for Britain as we leave the European Union.”
11.30am update: Michael Gove supports Chequers deal ‘for now’
Michael Gove has offered a lifeline to Theresa May by saying her reviled Chequers Brexit deal is acceptable – “for now”.
Asked if it was permanent, he told BBC One’s The Andrew Marr Show: “Yes, but there’s one critical thing, a future prime minister could always choose to alter the relationship between Britain and the European Union.
“But the Chequers approach is the right one for now because we have got to make sure that we respect that vote and take advantage of the opportunities of being outside the European Union.”
Mr Gove said the responsibility was now on the European Union “because we’ve shown flexibility”.
11am update: Khan slapped down over Brexit rerun demand
Labour MP Barry Gardiner has trashed calls for a second Brexit referendum just hours after Sadiq Khan said he would support the idea.
Speaking on Sky News, the Labour MP said: “To have a second referendum would be to throw this Government a lifeline.
“I think the right thing to do is say ‘if this Government cannot do what it is supposed to and govern then we need to change the Government.’
“Calling for a second referendum is really giving her a lifeline because then she can say ‘well if I can’t get it through Parliament I’ll go back to the people.’”