David Boothroyd's site provides a list, but it has not been updated for a while.
If we look at continuous service, then we have 2 MPs - both Prime Ministers - serving for over 50 years. David Lloyd-George for 20,032 days and Edward Heath for 18,709 days.
After the May 2015 general election, with Peter Tapsell, the Father of the House of Commons and Conservative MP for Louth & Horncastle, retiring, the longest-serving MPs will be a group first elected in June 1970 - Ken Clarke, Conservative MP for Rushcliffe; Gerald Kaufman, Labour MP for Manchester Gorton; Michael Meacher, Labour MP for Oldham West & Royton; and Dennis Skinner, Labour MP for Bolsover.
They will reach Heath's record on 6 September 2021, while having to wait until Easter Monday 21 April 2025 (which - under current timetables - lies in the 2025 election period) to reach Lloyd-George's record.
Hence, any of them re-elected at the 1 May 2025 general election (their 14th successive victory) would take his seat as the 20th century's longest continually-serving MP. Looking at that timing, would any of them, if re-elected in 2020, want to announce their retirement at the end of that Parliament, knowing that on dissolution (when they would cease to be MPs for the final time) they would be just 4 weeks short of breaking a record? The option to accept a peerage in a Prime Minister's Resignation Honours List which would follow the election if there were a change in Government could be there to enable them to break Lloyd-George's record and retire in the summer of 2025.