As luck would have it, I'm writing a long article/short monography on the P.1121 for publication later this year.
The P.1121 has its origins in Hawker's P.1103 proposal to F155/T (OR 329), as a dedicated high altitude interceptor. Hawker's proposal wasn't popular, as it was more realistic (and hence lower performing) than some of the others. However, Camm was encouraged by some to redesign the P.1103 for the strike role, which became P.1116. P.1121 was seen by Hawker as potentially a dual purpose machine, a bit like a US "Phantom". Unfortunately, the UK was obsessed with hugely ambitious projects to intercept Mach 3 bombers at 80,000ft (OR 329), and strike over huge distances (GOR 339), and Hawker were unofficially encouraged to spend their own funds on P.1121 as a "fallback" just in case budgets for the other projects were cut.
In retrospect with official backing P.1121 could have been a great Hunter followon, and a rival to the Mirage III, Phantom II and MiG-21.
Available now: my book Hawker P.1103 and P.1121: Camm's Last Fighter Projects from Blue Envoy Press