Britain's Conservatives have been divided for decades over Britain's membership in the European Union, and the draft withdrawal agreement has infuriated the most strongly pro-Brexit members, who want the country to make a clean break with the bloc.
British media also reported that several pro-Brexit senior Conservatives, including House of Commons leader Andrea Leadsom, are working to persuade May to change her Brexit plans and renegotiate the divorce deal to make it more acceptable to them.
May and added, "I think it's absolutely vital that we focus on getting the right deal in the future and making sure that in the areas that matter so much to the British people we can get a good outcome".
May because both are among the few cabinet ministers left who represent the hard-Brexit wing of the Conservative Party, which advocates cutting nearly all ties with the EU.
"I think there's still the potential to improve on the clarification and on some of the measures within it and that's what I'm hoping to be able to help with", she said.
So far, more than 20 Conservative MPs publicly admitted to submitting such letters, with others thought to have done so in private.
Labour whips are now confident, however, that very few - if any - Labour MPs will back May's deal because they have concluded it would also be disastrous for their constituents, leaving Britain locked into the EU's economic system for the foreseeable future but with no say in setting the rules that govern it.
A Remain supporter during the 2016 referendum, Ms Rudd has given her backing to Mrs May's draft Brexit agreement, saying it is "not ideal but flawless was never on offer".
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Mark Francois, who has also sent a letter, said May's plan would leave the United Kingdom "half in and half out" of the European Union and claimed no-one expected her to get it through Parliament.
The party's shadow cabinet office minister Jon Trickett said: "After enforcing Theresa May's hostile environment in the Home Office, Amber Rudd will now be in charge of the DWP's hostile environment for disabled people and the poorest in society".
As they campaigned for the 2016 referendum, anti-EU politicians knew they couldn't rely just on the minority of voters who prized sovereignty over the benefits of trade integration.
Mundell said he has reservations about the draft deal but other alternatives were "even more unpalatable".
Ireland's foreign minister, Simon Coveney, said on Saturday that British pro-Brexit ministers were "not living in the real world" if they thought they could renegotiate the divorce treaty agreed with the European Union last week.
The Brexiteer also told Mrs May her draft agreement with Brussels "doesn't stand a cat in hell's chance of getting through parliament", while further Tory MPs also stated their opposition to the deal.
The plans include "buffer stocks so that we have all the logistical capacity that we need to carry on running our business", said Chief Executive Warren East.
And if she wins it no one in her party can challenge her again for a year. It is said this could be reached next week, though there is doubt whether there would be enough support to unseat her.
Both sides have agreed at a technical level on a draft deal for Britain's exit from the EU.