The trip has not gone down well in currency markets, with the pound falling to a day's low of $1.2591 in early European trade.
After surviving a no-confidence vote by her Conservative Party on Wednesday, May asked EU leaders at a summit in Brussels for political and legal assurances that she said could convince the British parliament to approve her deal.
But German Chancellor Angela Merkel and French President Emmanuel Macron ruled out any reopening of last month's treaty aimed at ensuring a smooth exit on March 29.
"Unless we get some radical political developments, the pressure on sterling will be to trade lower," said Simon Derrick, chief FX strategist at BNY Mellon in London.
However, the British currency was broadly flat against the euro at 89.70 pence as weak European PMI data pushed the single currency lower.
On a weekly basis, the pound is set for its biggest drop in seven weeks as the currency markets digested the tough task that May had ahead of her to win concessions from the EU over her Brexit deal.
Sterling is still near the bottom of its recent range and traders say a 20-month low of $1.2477 hit on Wednesday will act as a temporary support for the battered currency unless there is further clarity on the outcome.
Though most investors think the British parliament will eventually back a "softer Brexit" rather than a clean break from the EU, traders have shied away from taking bets in the currency markets.