No, ATC is not responding in procedural ways to either the mayday call or the airspace violation. National aviation regulators were likely aware of this trip and its exact course well in advance, there is likely some way to control the balloon, and legitimate interference with actual air traffic would have meant arrests of either James, the producers/BBC executives, or both.

You do not fuck around with aviation regulation. Nobody's letting an idiot in a balloon potentially endanger the lives of hundreds of people on commercial airliners in the most critical phase of flight, and ATC and law enforcement are not going to be that nonchalant if said idiot did so anyway.