If you want to use your birth name at work, you need a matching bank account so you can be paid that name. You will need to check that your NI/tax record tallies up (it works from the number, not the name, so should be OK, but it's always good to make sure it's in order than have a nasty shock later) plus you need to check pension name.
It helps if you make your own travel bookings, if your passport is in new name, because it reduces error (as admin staff might forget you have two names) and it really helps if you have a credit card which matches your passport.
It is a bit of a PITA to run two names without hitches. But it's totally possible, you just need to check it's set up in a way that is friendly to The System and works in a way you are happy with.
I chose to stay with my birth name on everything, and don't really use my married name at all. If I want to use it socially (as you do domestically) then I just use it with no supporting documents (as no-one ever needs to check and I found that way round to be far simpler).
My DMum did this back in the 50s, btw. It was considerably easier then, as her job did not involve foreign travel, and identity checks were nowhere near as extensive.