American Thanksgiving time period is a slow travel period for TATL flights including business/first class. Most Americans don't want to travel to Europe for business during that time period and most American businesses are closed so no need for European business travelers to be coming to the US during that time period unless you are visiting family in the US.

That's why they have business class sale to/from Europe every year during that time period. You will have to wait until 1-2 months before Thanksgving to see what the fares are going to be like. If OP is flying from FL, I would say BA, VS and AA are the main airlines with direct flights from MIA and/or MCO to London. Other arlines will match the sale, but you will need to make a connection or two.