Thanks, as you've mentioned this figure is really annoying for several reasons.
I've never once seen a good reference for now it's been calculated, it seems to have sprung from thin air and just gets repeated ad nauseum.
It also hasn't changed since I was applying for university, when inflation (granted public sector inflation is less than whole-economy inflation I'm led to believe) most certainly has.
Furthermore, whatever the true sum is, it's not like it disappears into the ether.
If we think where the money to fund undergraduate medicine comes from, it's pretty simple - in England, it's from NHS England (formerly Health Education England).
It goes to universities. They use it (and the standard £9k/year for the first four years) broadly for three things - the costs of running the academic aspects of undergraduate medicine, paying trusts/GPs to have us on placement, and 10% I understand goes into widening participation initiatives.
I'm not convinced my course was that expensive to run in the first two years. We had ~25 academic staff deliver the first two years of our course. So, not dissimilar to my friends who did science degrees. We had course-specific teaching facilities and resources. Again, so did friends on other courses. Indeed, many of them had labs and used very expensive consumables. But the university could pay for that without extra funding (or likely by fleecing those on courses cheaper to run).
Now, money to trusts/GPs for placement. Remember, this is effectively money from one part of the NHS to another. I don't know how much it cost to have us, but I can't imagine it's £225k over three years. So this is a funding stream for trusts (and one of the reasons teaching hospitals were traditionally more 'prestigious' and why every trust is rebranding itself as 'University Hospital of St. Elsewhere's'. In terms of teaching in the latter three years, this was delivered by consultants. Each week we had two hours split between 5 of us with a consultant for a tutorial, and half a day of tutorials delivered by consultants. My uni bragged about how intensive the teaching we had with consultants was so I imagine that's fairly typical of everywhere.
So where does the rest of this money go? If you have a "proper" professor as a consultant, their full job title will be "Professor of X and Honorary Consultant in Y". They split their time between research and clinical practice. They are employed by the university and my understanding is the majority of them also have their clinical time paid for by the university. Their research is also funded in part by the university (and otherwise from grants/legacies).
In fairness, there are also clinical teaching fellows who are doctors who spend a proportion of their time teaching medical students, and the rest working as normal junior doctors. Where I trained, they were employed (and paid) by the university for both their clinical and teaching time in a similar manner to above, but where I work now they are jointly employed (and paid for) by the university and the trust.
So essentially the £250k is made up. And whatever the true figure is, a small proportion is actually spent training doctors - the rest is just another funding stream for trusts from NHS England.