However, Mrs May defended her Brexit plan as she embarked on a visit to Wales and Northern Ireland on Tuesday.
The prime minister insisted the 26-page political declaration on the future EU-UK relationship, agreed alongside the UK’s withdrawal agreement, meant “we will be able to negotiate trade deals with countries around the rest of the world”.
Visiting the Royal Welsh Winter Fair in Builth Wells, Mrs May also claimed the UK and US are already “working very well” on the terms of a new trade deal.
She added: “As regards to the US, we have already been talking to them about the sort of agreement that we could have in the future.
“We have a working group set up and that is working very well, has met several times and is continuing to work with the US on this.”
With Mrs May expected to visit all regions of the UK during the campaign to sell her Brexit deal before MPs vote on 11 December, the prime minister travelled on to Northern Ireland later on Tuesday.
After meeting business leaders, young farmers and students at Queen’s University Belfast, Mrs May held talks with Northern Ireland’s political parties.
However, her meeting with DUP leader Arlene Foster – whose party props up Mrs May’s government at Westminster – appeared to have little success in softening opposition to her Brexit agreement.
Following the talks, Ms Foster repeated her demand for the prime minister to ditch the so-called backstop arrangement for the Irish border, despite Mrs May having insisted Brussels will not accept it.
Ms Foster said: “The EU will obviously say there can be no change right until the moment they accept change.
“Presently there is absolutely no pressure on them to shift their position because the UK isn’t even asking.”
The DUP leader had earlier branded Mrs May’s visit to Northern Ireland as “a waste of time”, telling Sky News: “Would it not be better to spend time now actually trying to get a better deal?
“Trying to get a deal we can all sign up to instead of wasting time going around the country for two weeks.”
Mrs May’s chances of getting her deal through parliament appear slim, with it estimated she could be more than 60 votes short of winning the House of Commons support.
Pool of support for May even shallower than first thought
The rebellion in the prime minister’s own party appears be hardening ahead of the crucial Brexit vote, writes Sky’s Tamara Cohen
Former defence secretary Sir Michael Fallon, previously a May loyalist, added to the prime minister’s woes when he branded her deal “doomed” and said he would not vote for it.
Ex-foreign secretary Boris Johnson also kept up his attack on the prime minister by rubbishing her plans to debate her deal on TV with Labour leader Jeremy Corbyn.
“There is no point having a debate with two people who voted Remain and deals that don’t take back control,” he claimed.
However, Mrs May did receive some support when Japanese Prime Minister Shinzo Abe welcomed the fact she had reached a deal with Brussels in a telephone call between the two leaders.
An early plan for selling a Brexit agreement, which was leaked before a deal was reached with Brussels, suggested Downing Street was hoping for the endorsement of world leaders such as Mr Abe.
On Wednesday, the government will publish economic analysis of various Brexit scenarios.
But, opposition MPs have demanded the government also publish the full legal advice on the withdrawal agreement in the next few days, following parliament’s backing earlier this month for ministers to make the information available.
The government also came under attack after Home Secretary Sajid Javid was unable to say whether plans for a post-Brexit immigration system will be published before MPs vote on the Brexit deal.