I've never heard any mention of a design from the Brits. Actually, the
design concept was quite simple. They did the entire aircraft based on
ballistic tests with a 50 Cal. bullet even to taking the canopy out of
the equation and replacing it with molded in windows.
...
The horizontal tail proved to be the only real issue and they changed
that to a slab tail to solve the shock issue.

--
Dudley Henriques

I watched one of the Nova series episodes about 3 weeks ago about
breaking the sound barrier (I rented it on DVD). They covered the
British and American attempts to break the barrier in fair detail, and
had extensive interviews with one of the engineers from Miles
Aircraft, the British firm that was asked by the RAF to develop a
supersonic aircraft. IIRC, the Miles' engineer said that they
concluded that the best fuselage design would be one modeled after a
bullet. He also said they figured a hydraulic actuated movable tail
would do the trick to stop the shock-wave induced control freeze up
that was killing so many pilots during the time.

It was said that an American team did go to England during the last
part of the war and met with the Miles' engineering group, and that
the Miles' group was going to go to the US afterward to see what the
American's had learned, but the Pentagon nixed their trip. The Brits
didn't like that one.

Anyway I can't remember the timelines here ... a few weeks before
Miles' was to begin actual prototype testing of their ship (which
looked very much like the X1, but with a different nose) their program
was cancelled. This was sometime shortly after VE day. It was
cancelled by a bureaucrat who had visited some of the secret German
aircraft development centers the Allieds had discovered (some buried
underground). There he had seen swept wing designs and somehow
concluded that sweptwing was the only way to go supersonic. He
cancelled the supersonic program because the Miles' design was a
straight wing.

After the X1 succeeded, the British went back a few years later and
developed a radio controlled 2/3 scale rocket plane of the Miles
aircraft. It broke the sound barrier too.

Great show, I'm probably not remembering it all correctly. I think it
might be titled "Faster than Sound".