I think it depends on the registry office and what day of the week you want to get married. My DH and I got married on a Monday in a tiny little village in Derbyshire, and we were the only wedding that week! We booked that a few months in advance, but you might be able to get one soon depending on where you want to marry.
The most important thing that takes time to complete is the 'bans' or giving notice to marry. Once you have chosen where you are going to get married and made a booking for the ceremony, you must call the council in which you and your DF live, and make a booking to give notice of your intent to marry. You have to do this since you are subject to immigration control.
You must have lived in the borough for more than 7 days before giving notice, which can be proven by producing council tax statements, utility bills, etc. You must also bring your passports/visas, and anything else they ask for.
Once you give notice, 15 days must pass before your ceremony can take place. You will have to go and pick up the certificates for marriage in person on the 16th day. You then take these with you on the day of your ceremony.
Please note that once you have given notice, you cannot change the venue, unless you go through the entire process again.
Make an appointment for giving notice NOW. I called my council (a highly populated borough in London) to make an appointment to give our notices two months in advance, and the first available appointment was a week AFTER my wedding. Needless to say, I freaked out and begged a lady in the Registry Office for an earlier appointment. Luckily, the woman in charge was a sweetheart and took sympathy on me and the fact that my family from the States had already purchased flights and all...
I'm not saying that you won't get an earlier appointment, just that this was my experience. I had not planned well ahead and found myself in quite a pickle.
Hope that this helps. Congrats on getting married!