You need to go to the British Consulate and they will go through with you the steps you need to take to get your passport renewed. The time it will take is dependant on how much of a backlog they have, and what option you choose. The more you pay, the quicker it is, but make sure you take your time going through the paperwork, as one tiny mistake can result in the whole process being set back by weeks. They are for some reason particularly strict about the size of photo you have and the way you look in the photo. For some reason your not allowed to smile these days as it's seen as an attempt to obscure your appearance. I thought that was rather bizarre but their in charge.