I married my American girlfriend by just coming to the USA and getting married. That's what my lawyer told me to do, it's the quickest way, then file for work permit etc.Work permit wait was 6 months.Green card was another 4 months, After two years of marriage file I-751 then permanant resident status with no restrictions. Make sure your passport has plenty of time left bring birth cert all schools qualifications. Welcome to America.
You can do the above, sure, but it is frowned upon, and wont always work. There have been cases where a UK citizen has gone to the US on the I-94 visa waiver from, got married to their partner, and applied for Adjustment of Status (AOS), and stayed in the US. Yes it is the quickest route, but it is far better legally to go the K1 or K3 visa route. Generally for AOS, you will need to prove WITHOUT DOUBT that you did not enter the US intending to marry, and that it was a spur of the moment thing. In some cases, your passport will be stamped with 'no AOS' upon your entry to the US, especailly if you mention a US Citizen boyfriend (and have a wedding dress with you!). The authorities do not really like this method, and seeing as the AOS would be only the first small step to legal permanent residence, it is best to do things 'by the book;, even though there will be a longer wait (generally 6 monthsish) and time appart sucks, it will set you up better in the long run. You can do it..but I wouldn't recommend it.
You can still travel to the US on an I-94 whilst the visa is being processed to visit your bf.
The below link has many postings on the pitfalls of this, and is a great site for any UK citizen who is planning on marrying their American partner and living in the US:
http://britishexpats.com/forum/forumdisplay.php?forumid=35