The cross-party Get Britain Out grassroots campaign group will deliver a letter endorsed by an estimated 50,000 supporters.
It is not known if Mrs May will be at home, and it is not usual for Prime Ministers to accept such petitions in person.
But the group sees the event as a chance to underline the anger felt at the “Chequers deal” for continued close links with the European Union, which Mrs May agreed with her Cabinet.
The group has compiled the names of the tens of thousands of people who got in touch online to confirm they agreed with a letter posted on its website by Get Britain Out director, Jayne Adye.
Ms Adye said a previous letter to Mrs May on the issue received only a “holding reply” from the PM’s communications unit.
The latest letter which Ms Adye says thousands more supporters have flocked to endorse, tells Mrs May that “the vast majority of the public do not accept your proposed future relationship with the EU.
“The Government’s White Paper does not deliver Brexit in any meaningful sense of the word.
“It is not what we voted for in 2016. It would not bring about any of the crucial benefits of leaving the EU.
“Tens of thousands of members of the electorate are rallied behind us as signatories to these letters to you, demanding you uphold the wishes of the great British public when they were led into the EU referendum by David Cameron.”
Ms Adye adds that her hopes the resignations over the Chequers deal of Brexit Secretary David Davis and Foreign Secretary Boris Johnson might bring Mrs May “to her senses” were dashed by the Government’s white paper detailing its proposals.
Tonight Ms Adye said: “Our grassroots supporters feel betrayed, forgotten, and let down by the current direction of UK-EU Brexit negotiations, which clearly do not reflect the mandate given by the EU referendum result.
“The Chequers proposal will keep us under European Court of Justice jurisdiction, limit our capacity to strike free trade deals, and keep us bound by the red tape of the Single Market.
“The great British public clearly believe in this country and what we can do when standing on our own two feet. We deserve a political class with this same patriotic conviction.
“If Theresa May and most of those in her Remainer Cabinet are unwilling to implement the biggest political mandate in UK history, they should step aside and allow someone to take over with true conviction and insight into all the opportunities we have for our global future – instead of encouraging Project Fear Mark II.
“They simply do not have their heart and soul in Brexit for the British people.”