We went to the Philippines Consul in Madrid, we live in Spain and were on a trip to Madrid. They did a manuscript amendment in a couple of hours. I think we just took the NSO copy marriage cert.
I checked on the internet there appear to be Philippine Consulate offices in London and Edinburgh. I could not see anything for Northern Ireland. Maybe someone else will know more.
This is the number for the Philippines Consulate in London. Maybe a call to them will tell you how it can best be done for you. Phone 020 7937 1600 (sorry I cannot delete the Skype link, three tries)