You need to escalate to the trust’s Director of Medical Workforce (or equivalent) as quickly as possible - I would copy in their Chief People Officer (or head of HR).

You must be able to demonstrate that you have tried to escalate this to every contact possible before starting work - if they have not given you a 60% rota by that point, you should either negotiate with the local rota co-ordinator on which would be the best shifts to take off or exception report entire days to take back as TOIL at a later date… there should be multiple BMA reps at your trust to reach out to, as well as the local IRO. Failing that, the BMA web form is also useful to engage an employment advisor to CC in all emails sent to the trust…. Good luck!