I don't know about CAA requirements, but the FAA would allow a PPL holder like you to acquire a jet type rating. Outfits like Flight Safety, SimuFlite, etc... assuredly would be more than happy to train you on a Biz Jet, like a Cessna Citation SP (Single pilot), as long as your credit cards are good. However, I doubt that any outfit would rent or lease a jet to a PPL holder,...unless you buy the jet.
