Congratulations! You survived the trials and tribulations to get here and finalized.
I don't have a UK passport, but I do have a USA and an Irish one. I had changed my name a few years back in the USA, but kept using my old name professionally, so didn't get anything official changed over for a number of years. I finally changed my USA passport name about a year before moving over here, once we had decided we were going to make the move. (Had to provide the court order, no big deal.) The Irish, unfortunately, have a thing where you have to have been using the new name for a set number of years before they will allow you to change your passport to it if you are not changing your name due to marriage. So, for a couple of years I had two passports in different names.
When applying for anything related to the UK, I had to use my Irish passport as I am here as Irish. Once I was here and established, I was able to change my name by deed poll and have everything (all the utilities, etc.) switched over to that new name by showing the deed poll.
Travel was interesting - leaving or entering the USA you are required to use a USA passport if you have one. So I had to always book everything related to USA travel in my USA name. I'd get on the plane USA passport, arrive in the USA on the USA passport, return leave on the USA passport, but land on the Irish one. I'm sure that's messed up someone's report somewhere, but I had no problems. I was always waiting to get pulled into a little room and grilled by ICE, but that never happened.
Anyway, changing your name by deed poll is quick, cheap, and works - at least it worked for the Irish government eventually so I would assume that having a deed poll with your new name on it might work for UK? Something to check out?