Upvote:5
Pretty much every private hire car company will be working over Easter. About the only exception will be sole operators, who you are unlikley to book anyway.
The terms to look for are either "Private hire" or "Minicab" - both refer to taxis that must be pre-booked and cannot be flagged down off the street. Around London there are a great many of these services. Proper "Taxis" or "Black Cabs" can be picked up without booking in advance, but will almost certainly cost more.