You can have it converted to the local CNI at the British Embassy and this can be done while you wait (20 minutes or so) and without making an appointment, but I believe that if you want to go to the British Consulate in Cebu you must make an appointment first.
The 10 days is the waiting period for the marriage licence and it depends on the province where you apply for your marriage licence whether it will be 10 days in total or 10 working days, counting only Monday to Friday as qualifying days.
Iain.