It's just take digging in government rules and arguing. As long as it's not the first UK passport it's doable.
My friend went round and round and sent many documents back and forth for over a year trying to renew her British passport, to no eventual avail. UK authorities were extremely unsympathetic and unhelpful. The offending "misnamed" foreign passport was long expired and French authorities required a valid British passport to renew it - she was left without any passport at all for over a year, until the French took pity and provided an alternate path to renew her French passport.