Mrs May had travelled to Brussels hoping to get assurances from 27 EU leaders that would help her silence her critics and get her Brexit deal through Parliament.
A key issue was the Northern Ireland backstop, but while leaders promised to do their best to ensure it is never needed, they told Mrs May they cannot re-open the terms of the Withdrawal Agreement.
European Commission president Jean-Claude Juncker said: “We don’t want the UK to think there can be any form of renegotiation, that is crystal clear.
“We can add clarifications but no real changes. There will be no legally binding obligations imposed on the withdrawal treaty.”
Mrs May also came under fire for a lack of clarity over what the UK wants from its relationship with the EU, with some accounts of the meeting suggesting that the Prime Minister was repeatedly interrupted by Angela Merkel asking her what she actually wanted from them.
“Our UK friends need to say what they want, instead of asking us to say what we want,” said Mr Juncker.
“So we would like within a few weeks our UK friends to set out their expectations for us because this debate is sometimes nebulous and imprecise and I would like clarifications.”
Mrs May’s visit comes after she survived a vote of confidence by her own MPs, and said she will not lead the Conservatives into the next General Election.
During her meeting in Brussels, Mrs May said she had to be able to convince MPs that the UK would not find itself tied to the EU indefinitely through the “backstop”.
“There is a majority in my Parliament who want to leave with a deal so with the right assurances this deal can be passed,” she said in prepared remarks released by No 10 Downing Street.
“Indeed it is the only deal capable of getting through my Parliament.”
She made clear a failure by EU leaders to offer concessions risked the collapse of the whole agreement with the UK leaving in March in a disorderly, no-deal Brexit.