I am no expert on that. Every junior doctor can get a starter job, regardless of where he or she trained, and AFAIK there are no duff medical schools in the UK. They all have high standards.
Later on, progress into a specialism depends on things such as doing well in Royal College exams, and it may be that some graduates have an edge over others when competing for positions as Registrars with top Consultant teams, and what not. Medicine, like every profession, has its high flyers and its backwaters.
In general, many (not all) Oxbridge graduates do well in their careers not simply because of being Oxbridge graduates, but because they tend to be people who have been high flyers throughout their educations and they continue to be so when in the world of work. The Oxbridge teaching system and intensity of study may also favour some career paths which have a high academic content.
In my world (commercial law), if my chambers tests two candidates university-blind about the law of contract, the Oxford graduate who has studied the law of contract with Oxford intensity may well outperform the non-Oxford graduate who did lots of optional modules and studied the law of contract at a more superficial level.
But I reiterate that every new doctor from every UK medical school can get a job as a doctor.