About a last will and testament - I can't speak about Britain but I just experienced this here in the US. My mother died 2 years ago when I was still legally "him". I have since told the law firm about my new name and they didn't even need the legal documents. However the final disposition of the will in legal documents now reads "Cara Elizabeth ******, formerly known as ***** ******** ******" (new name, formerly known as old name). Apparently this is very common especially for women who get married and whose last names change so my name change got treated exactly the same. I don't even consider this "outing" myself as no one except my sister and the lawyers will be present at the final reading and the filed document will go into some dusty county clerk file cabinet in a part of the country I'm not sure I'll ever visit ever again.
I highly doubt that Britain is any different as there are lots of legitimate reasons to change a name and the name change documents make it clear that you are still you, and are still the same person named in any financial instruments.
So it sounds like an excuse to stop you rather than a real excuse.