Defence Medical Service already exists:
The Defence Medical Services (DMS) includes the Headquarters Surgeon General (HQSG), Joint Medical Command (JMC), Defence Dental Services (DDS) and the three single service medical organisations. It is headed by the Surgeon General (SG).
Medical, dental and related support services are provided to armed forces personnel by the Ministry of Defence (MOD), the NHS, charities and welfare organisations.
I addition the newly formed Joint Forces Command (JFC) stood up recently:
We work toward making military operations successful by making sure joint capabilities - like medical services, training and education, intelligence, and cyber-operations - are efficiently managed and supported. We also communicate actual experience in operational theatres so that it can be reflected in top-level decision making.