"We have been consistent in our condemnation of the actions of the Venezuelan government and in our unwavering support for the National Assembly as a democratic institution," May said after the meeting.
The meeting is the latest in a European tour that has seen Borges meet with French President Emmanuel Macron on Monday, Spanish Prime Minister Mariano Rajoy on Tuesday and German Chancellor Angela Merkel on Wednesday.
Borges leads the opposition-dominated assembly that President Nicolas Maduro has effectively shut down.
"Today's meeting is an unambiguous signal that the UK will continue to work with our international partners to put pressure on the authorities to decrease tension in Venezuela and prevent the country from being taken further away from democracy," May said.
The prime minister also expressed "great concern" for the continued detention of opposition leader Leopoldo Lopez, whose mother accompanied Borges on the trip.
"I once again urge the Venezuelan government to ensure that human rights, the rule of law, the separation of powers and the integrity of democratic institutions are respected," May said.