If you miss your flight, they will rebook you at your cost. "Your cost" often times means the walkup price for a ticket, whether thats in Biz or Coach is upto you based on what you are willing to pay. Walkup price for a biz JFK-LHR can be north of 10K.
If I were you I would a) either rebook now, before it costs you big bucks, or b) skip the meeting and make the flight.