The car starts fine when cold. When hot it takes many cranks to restart. I originally traced the problem to the coil, so I replaced it with a new Lucas coil Any ideas?

 

Fuel vapourisation after heat soak possible. Is your cooling system up to snuff? What is your operating temperature?

 

Does sound like fuel vapourisation. With engine off there's no flow in the fuel lines, so residual heat from the engine vapourises the fuel trapped in the fuel lines / carbs. It's common on many 'classics'. I bought a heat shield (fits between the engine & the carbs) for my Triumph GT6 - solved the issue nicely.
Also getting it on my 4.2ltr Mk2, but only takes a few extra cranks as it sucks the new fuel through so not a real issue (also helped by having a louvered bonnet!!!).

 

Next time you come home from a good run, pop the bonnet open and check restart after 30 minutes. This solved problem on my XJ6; my XKE had louvered bonnet no issues.
Rgds
David