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No, training is part of the role that you perform and it's part of your employment. The minimum wage (or your contract terms) cannot be ignored.
It would be difficult to say that somebody is actually on a 24 hour shift. If somebody is "on-call" this can amount to being part of their job and therefore require payment at the minimum statutory rate at least. It depends whether, whilst "on call" you're free to do other things really, and if not, then you could be held to be entitled to your hourly rate during this period.
Then yes, this does sound wrong to me.
There is a national helpline where you can get more information about this and make a complaint about working practices: https://www.gov.uk/pay-and-work-rights-helpline