Two groups of Tory MPs will launch campaign groups later aimed at shaping the future direction of their party.
Work and Pensions Secretary Amber Rudd is among those backing One Nation Conservative Caucus, a group opposing a no-deal Brexit.
Former cabinet minister Esther McVey will launch Blue Collar Conservatism, aiming to target “working people”.
The contest to replace Theresa May has – unofficially – begun, with several figures already saying they will run.
The prime minister has promised to set a timetable for the election of her successor after the next vote on her Brexit plan.
MPs are due to vote on the Withdrawal Agreement Bill – required to put the PM’s deal into UK law – in the first week of June.
Ms McVey, who quit as work and pensions secretary last November in protest at Mrs May’s deal, has already announced she will stand in the forthcoming leadership contest.
On the Blue Collar Conservatism website, she says the new group will aim to target “voters and communities most neglected by Labour”.
The Conservative Party “must do more if we are to genuinely speak for the people who need us most”, she adds.
“The concerns of people about the number of police on their streets, the quality of their children’s schools and the difficulties in getting on the housing ladder are palpable and must be addressed if we are to genuinely create a country which works for everyone”.
According to the Mail on Sunday, Ms McVey will embark on a “pub tour” campaign, calling for the foreign aid budget to be pegged to 2010 levels and the HS2 rail project to be scrapped.
Meanwhile, the One Nation Conservative Caucus is expected to publish a list of demands for whoever wins the Tory leadership race.
The group is also expected to call for further action on climate change, and reportedly aims to block any candidate who backs a no-deal Brexit.
Analysis by Ben Wright, BBC political correspondent
The unofficial contest to replace Theresa May is already up and running, with candidates declaring their desire for the job and policy platforms being set out.
Work and Pensions Secretary Amber Rudd has not – yet – thrown her hat in the ring but spearheads a 60-strong block of Tories called the One Nation Caucus.
On Monday, it will launch a declaration of values that seeks to cement the post-Theresa May Tory Party in the centre ground.
Sources deny it’s a “stop Boris Johnson” effort, but the group is emphatic there must be no future coalition between the Conservatives and The Brexit Party and is stressing the importance of issues like the environment.
Amber Rudd, who will speak at an event to launch the group, has said it is “entirely possible” she will launch a bid for the leadership once Mrs May steps down.
The group also includes MPs such as International Development Secretary Rory Stewart, who has confirmed he will put himself forward to be next Tory leader.
Conservative MPs Nicky Morgan, Damian Green and Sir Nicholas Soames will also make speeches at the event.
Former Foreign Secretary Boris Johnson has also said he will run for the leadership, telling an event last week: “I don’t think that is any particular secret to anybody”.
Former Brexit Secretary Dominic Raab, Health Secretary Matt Hancock and Chief Secretary to the Treasury Liz Truss will speak also at a Telegraph event on the future of the Conservative Party later this evening.
All three have been tipped as contenders.
In a Conservative leadership contest, MPs hold a series of ballots, with the candidate gaining the fewest votes eliminated at each stage.
Once the field is reduced to two, the winner is chosen by a vote of party members.