Can you really possibly apply for FLR without even amending your passport?
YES
.... altho' you might want to amend the name in your passport, from your single
to married name..... then it might be clearer to the admin people at the UKBA
as to why your married name is also on the FLR form.
(Believe me, they are THAT stupid ! )
Also, you'll have your married name on some "official" document... ie, your passport.
As you're in Kent, u could pop into the Embassy and get it done in a few hours.
(the name amendment is merely another written entry into your existing passport,
with an official stamp)
.... and register your marriage at the same time (a requirement of the Philippine Govt).