Phillip Cowley, Professor of Politics at Queen Mary has written about a research project which involved sending MPs emails from imaginary people, to see how they might respond. This project involved sending marginally different letters to test whether a certain type of person might be more likely to receive a response from their MP than another. He writes: "This project, carried out in 2019 with a very similar research design and which ended up in one of the top academic journals in its field. It found British MPs had a really high response rate to queries from their constituents, with 91 per cent responding (good news), albeit with some bias in their responses, depending on who it was they thought was writing to them (less good news)."
This was covered in The Conversation