No, the allocation of funds for the STP is the responsibility of the local commissioner and the employing Trust. The use of the training budget is down to agreement within the department you are working in.
For in service candidates, the local employer is responsible for considering any issue of pay protection or payment at a higher salary for the duration of the training where applicable.
Determining eligibility under the Widening Access Training (WAT) scheme is the responsibility of the trust which employs you. You should contact your HR department directly as only they can establish whether you are eligible and arrange a refund via their payroll system if you are. You can find more information on the WAT scheme on the Gov.uk website and from NHS Employers.