Good news now, though: after more than a year of endless prodding by yours truly and hard work by various people in the Lords, the new passport name guidance is here, and it allows people to obtain a passport in the name of their choice if they can prove that their foreign citizenship doesn't allow them to change their names and also demonstrate that they are now using their desired name 'for all purposes' (which in Britain is easy: take a marriage certificate into the bank and they'll change your account name within minutes). The new policy specifies that in such cases a note in the British passport will explain that the holder is also known by their other name on their foreign passport.
This also helps transgender people whose non-British citizenship doesn't recognise gender changes.
Without further ado, here is the new name policy page, which contains two pdf documents:
https://www.gov.uk/government/publicati ... e-guidance
In the first pdf, "Use and Change of Names" (click on "Change of name guidance"), the relevant portions are paragraphs 26 to 28. They allow the issue of a British passport in a name other than that on a person's foreign passport if the person can prove that the foreign country of which they are a citizen won't allow them to change their names, and that they have been using their new name (the name desired on the British passport) 'for all purposes'.
In the second pdf, "Annex A: Use of Names in Passports", the relevant sections are paragraphs 6.5 to 6.7. They reiterate the material from the first pdf, provide a few more details, and specify that in such a case, an observation will be placed in the British passport explaining that the person is also known by their other name on their foreign passport.
The new documents also make provision for people who have trouble changing their names on their foreign passports because this would require them to travel to the foreign country to change their passports, but the standard there (Annex A, paragraph 6.7, part iii) is that the person would have to be 'placed at a high level of risk' in order to travel to their other country of citizenship.
For those of you who are affected, I suggest mentioning these two documents, and the relevant portions thereof, in your passport application and even printing out the operative pages (two pages from each document, so it won't be a matter of sending reams and reams of paper).
I really hope that this finally solves the problem of the increasing number of people who, through no fault of their own, were having problems obtaining a British passport in their desired name just because their foreign citizenship didn't allow any alteration to their name.
Good luck to us all!
