Let's start with defining your US visa options: K-1 or K-3. Both take at least five months to file for if your case is straightforward with no criminal history, medical problems, messy divorces, overstayed visas and the like. A more complicated case, mistakes in your paperwork, or new US immigration laws being passed while your petition is in process will add more time.
K-1 is the fiance visa. It is used if you want to come to the US, marry, and stay.
K-3 is the spousal visa. It is used if you are married and want to come to settle with your spouse in in the US.
Both visas have several stages:
The petition to apply-this is where the US citizen petitions the USCIS to allow their fiance/spouse to apply for the visa. This is done with form I-129F in a fiance visa and by form I-130 (and I-129F too) for a spousal visa. At this stage, there are several things which must be proven to the satisfaction of the USCIS service center: that the relationship is genuine, mostly.
The NVC: If your petition is approved, then it is sent to the national visa service center, who ships it to the US consulate in London. They mail out the actual visa application to the foreign spouse. There is more gathering of information and a medical exam; when the fiance/spouse has all the relevant information collected and forms filled out they return the application to the Consulate. The Consulate then schedules...
The Interview: this is the last and probably most nerve-wracking stage. The foreign fiance/spouse is called for a face to face interview. At this interview, the consular officer will question the potential immigrant. They will ask for proof that the US Citizen can support them, ask questions to determine if the relationship is genuine, and in general issue or deny the visa.
These are the same for both US visas. Now, onto your case. You have several options, all with different benefits and drawbacks.
1. Marry in the UK and wait out the process together. This option is expensive, and can only be used if he has an address in the US (this is called maintaining domicile), as the USCIS will not process a visa application for someone who does not have US domicile (for US citizens who live abroad there is something called Direct Consular Filing, but as your fiance doesn't live abroad and cannot establish residence, it doesn't apply to you). He would have to fly back to the US, apply for and receive a fiance visa, fly back to the UK, marry you, and switch to Further leave to remain. All of that costs a pretty penny, but this is the option with the least time apart. Once you have his further leave to remain, you can file for the K-3 spousal visa, which takes at least five months and more if there are complications or if the USCIS is busy.
2. Marry in the US on the Visa Waiver Program. This option is if you want to get married NOW in the US. You cannot remain in the US after getting married on the VWP-you must return to the UK within 90 days of entering the US or risk complications (like a ban). After you marry, your husband can then begin the process of applying for your K-3 visa. The advantage to this method is that you can have a US wedding NOW, and you are only filing for one visa so costwise this is less expensive than option one. The drawback is that you have to go home and wait for the visa to be processed (you can visit, but as you have a US spouse at that point you are "flagged" as a possible candidate for overstaying your welcome!) so you have time apart.
3. Apply for the K-1 fiance visa and move to the US. Basically, this would entail much the same as the K-3. The difference is he would have to file for the K-1 before you could come to the US permanently. It is less expensive than the first option, as you don't need him to get UK visas issued, and takes about the same length of time as the K-3 to be issued. The drawback is that there would be time apart unless he can stay in the UK with you for the length of time it would take to be processed AND he stil has a US address (and someone trustworthy to get and forward his mail to you!). This option would give you less time apart than marrying in the US and filing for the K-3 provided he can afford to stay in the UK with you.
I hope that clears things up.