Thank you @goodbyestranger that's encouraging. He definitely plans to apply for the ones at Cambridge and UCL. There are other research groups in the relevant field (Oxford, Imperial, Manchester, Sheffield) but he needs to balance time devoted to applications with studying Part III, which is quite a demanding course. Also it might be a bit hubristic to apply to Cambridge, Oxford and Imperial?
His Part II marks were all strong but unfortunately his only 'wow' results were in papers which aren't related to the type of physics he wants to pursue.
He does also have a plan for if he can't get a funded PhD place: applying for the scientist training programme through the NHS.