Hello Grace05 welcome to the forum!!
Yes, I think you need to contact Philippine Embassy in London (consular services)http://philembassy-uk.org/contact.html for the registration of marriage (NSO)as they will require this registration when you amend your passport to your married name in the future.
and yes,you can also register the birth of your child Fil/Brit/Irish/Icelandic or any foreign national parentage with the Philippine Embassy if one parent was still a Filipino citizen at the time of birth of the child.
