Because you entered under the Visa Waiver Program, you gave up many important rights, including the right to change status in the US. Whether you would be allowed to adjust your status in the US would therefore depend on the policies in effect at the office that would adjudicate the Adjustment of Status. Some offices allow it, some will deport you.
Additionally, once you are married, you will not be able to travel under the Visa Waiver Program.
The proper way to do this is to either:
1) Apply for a fiancee visa. Enter the US with that visa. Get married within 90 days of entry. Then apply for adjustment of status.
2) Get married and file the I-130. Leave the US and process for an immigrant visa in the UK after the I-130 has been approved.
You should retain an experienced immigration lawyer to review all the facts and advise you accordingly.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship.