There's plenty of similarities: both are Tories; May is only the second female Prime Minister after Thatcher; and both have an air of "properness."
Thatcher was known as the Iron Lady, while the Telegraph has called May and "ice maiden."
But the Prime Minister thinks comparisons with Thatcher, who was Prime Minister from 1979 to 1990, are "lazy," according to an interview with May in the Financial Times.
The FT spoke extensively to May's Tory party colleagues and others who work closely with the Prime Minister and claim that she tells aides she dislikes "lazy" comparisons to Thatcher.
Donald Trump wants to recreate a special relationship with May of the same kind Thatcher had with Ronald Regan in the 1980s. But May told the FT: "I've never thought of myself like anybody else, or as doing the job like anybody else."
An unnamed cabinet minister also told the paper that May is not perceived in the same way as Thatcher was within the Tory party, saying the Conservatives have "changed a bit from the days of Thatcher worship."