The Typhoon can take off in 8 seconds from releasing the brakes and be supersonic in 30 secs. So I guess it would take 2 to 3 minutes to reach Wetherby and a height where he could go supersonic without too many complaints.
I had the good fortune to fly supersonic on Concorde some years ago. The most notable thing, apart from arriving quickly, was the flying height of 60,000 ft where the light was a purple sort of colour and you could see the gentle curvature of the earth.