Joan Ryan also said polls show the Conservatives heading for a "large majority" and that "no one thinks Theresa May will not be Prime Minister", before begging local residents to vote for her despite "misgivings about the Labour leadership".
The document, passed to the Guido Fawkes blog, is a blow for Labour in London just a day after a stunning poll showed Mr Corbyn as preferred choice for Prime Minister among Londoners for the first time.
Ms Ryan, who served as a Home Office minister under Tony Blair, wrote in her letter that local residents told her, "they have more confidence in Theresa May as Prime Minister than they would have in Jeremy Corbyn.
"The polls are all saying that the Conservative Party will win a large majority, possibly with more MPs than they have ever had before. Realistically, no-one thinks Theresa May will not be Prime Minister, or that she will not have the majority she needs to negotiate Brexit."
She then makes a pitch for constituents' votes by claiming that having her in the House of Commons will help limit the scale of the Tory majority and the potential damage she claims it might do to public services.
Ms Ryan, who won her seat by just over 1,000 votes in 2015, adds: "That's why whatever your misgivings about the Labour leadership, I hope that you will consider voting for me as your local MP."
A poll by YouGov for Queen Mary University of London showed that Labour has surged in London opening up a 17-point poll lead over the Tories.
Asked who would make the best Prime Minister, 37 per cent picked Mr Corbyn and 34 per cent Mrs May. A survey taken just after the manifesto launches last month had Ms May ahead by 38 to 32.
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