The Prime Minister, and other government ministers, naturally have the time they can dedicate to constituency matters limited by the duties of their roles in government. However, as an important part of an MP's duty is to represent their constituents, this is never completely ignored.
Anecdotally, the website of the current Prime Minister, Boris Johnson, allows members of his Uxbridge constituency to book a ten-minute appointment, and states that he holds advice surgeries across the area. The 'News' page of his website also seems to document most of his constituency appearances.
In general, tasks such as responding to correspondence, following up and providing briefs on local issues, local media management, and organisation of constituency events is handled by a constituency office, and a large proportion of correspondence from constituents is not be seen personally by the Prime Minister.