Section 157 of the Criminal Justice Act 2003 requires the Court to obtain and consider a medical report on a defendant who is, or appears to be mentally disordered, before passing a custodial sentence.
HM Courts and Tribunal Service commissions the reports for the court and the payment is from central funds (the Costs in Criminal Cases General Regulations 1986). Reports and recommendations go back to court.
In practice, the court Legal Advisor/Court Clark dealing with the case will send the request to a psychiatrist and the court will pay the psychiatrist.