Everybody in the UK has a right to access healthcare - most people do this through the National Health Service (NHS), which is free at the point of access. This means that for most medical procedures, you do not have to pay. Many trans people choose to medically transition through the NHS, and can do so successfully. They cover diagnosis of gender dysphoria, hormone prescribing, top surgery (the removal of chest tissue for people who are assigned female at birth (AFAB)), and gender confirmation surgery or bottom surgery. 

No medical professional has the right to refuse you treatment based on your trans status and doing so is a breach of the Equality Act (2010). You should receive fair and equal treatment, and should not be subject to any discrimination while under the care of a medical professional.