There was a very similar thread about this recently; the search box may turn something up that's useful to you.
The consensus in that thread as I remember is that a lawyer may help, however there aren't that many lawyers with experience in sorting the PL name change to match the UK change.
will Poland let me change my name on my Polish passport, if I change it in the UK,
It would, however name changes in Poland are fussier and require a court decision.
transition reasons
That shouldn't make any difference, not least because people in PL who've transitioned often change their name. TransFuzja, the organisation led by Anna Grodzka may be able to advise.