You need to apply for an ESTA. You cannot enter the US without one.
However, what will happen is your ESTA will automatically get cancelled on the day of the flight due to being British and obviously banned. You then clear immigration, from the US immigration officer, by proving your exemption so ensure to take evidence (marriage certificate). Then when checking in the check-in staff call US border control to request an ESTA manual override code. They then manually reinstate your ESTA at check-in
So, if you have no ESTA you will not be allowed entry. Also, very important, do not fill in your advanced passenger info into your airline and especially do not do advanced check-in. It's imperative the check-in staff deal with your check-in. You won't be alone.
Apply for the ESTA online as you usually do.