He claims K "had to tell the officers investigating the break-in that his fingerprints would be found in the house as he had been sleeping there with Ms A while George was away".
He believes Ms A was "not just personally involved with the officer but was his agent inside the Bradford branch of Respect, passing on gossip and lies damaging to George and Respect".
Mr Galloway also alleges that the officer used his official Scotland Yard email address to tell Ms A that he had evidence of voter fraud in the by-election which Mr Galloway won with a majority of more than 10,000.
Email accounts set up in false names were then used to "pump out false information to national newspapers" and to attack the MP on Facebook, he claims.
Mr Galloway said the aide's home in Bradford had been raided yesterday morning, and that a parliamentary laptop computer had been seized.
He added: "I have incontrovertible evidence. He either did this as a freelancer or it was sanctioned by his superiors. I have asked the Home Secretary to act on this."
In a letter to Mrs May published on his website, the MP said he had been the victim of "a campaign of vilification - a dirty tricks operation - using police facilities and resources".
The Met said the complaint had been passed to the Independent Police Complaints Commission and was also being investigated by its internal directorate of professional standards.