The UK can refuse to issue a replacement passport provided that it does not leave an individual stateless
If the person currently holds a UK passport solely and does not choose to take out dual-nationality with a Scottish passport, then not reissuing it
would leave them stateless, no?
Edited to add: Of course, once Scotland is independpent and the rUK has left the EU, we'll all be clammering to get Scottish passports so as to avoid applying for visas everytime we wish to cross the Channel!