Just wanted to make sure that you are aware that most foreigners need a "Marriage Visitor Visa" to get married in the UK (even if they are a US citizen or otherwise eligible for visa waiver) and you have to give notice at least 30 days before you get married. If your fiance is in the UK on visa waiver then he won't be able to give notice to get married and there is really no way to do quick weddings in the UK (less than 30 days). There is more information here: https://www.gov.uk/check-uk-visa/y/usa/marriage
As an alternative, you could get married fairly quickly and easily in Canada, Gibraltar, or Denmark on tourist visas for both of you. The other alternative if that you could do an online Utah wedding and then file your I-130 for a spouse visa after your fiance has had a chance to visit you. If you do an online wedding, there is a requirement that you have met in person afterwards to consummate.