Yes you used to be able to renew a passport through the embassy and it went off to New York and then Washington but they changed everything and passports can only be renewed or issued through the passport office in the UK.
So what... live without cedula and residencia for 3 months and pay the fine... its less then $100.... if your complainting about $100 come clean my toliets for a month I will pay you....
If your UK passport recently expired you can have it extended for 12 months at the UK Embassy/Consulate in Santo Domingo.There are some countries however, like the US that do not recognize an extended passport...... check it out here https://www.gov.uk/get-an-emergency-passport-extension-or-child-travel-document
Good luck......
Bryan
I renewed my residencia a couple of months ago at Migracion in Santo Domingo. The requirement was 6 months validity of your passport, mine had only 4 to go but they accepted it.