Doctors who specialize in treating transgender patients tend to follow the WPATH guidelines. On the plus side, you know the doctor has had some training about dealing with trans patients, and you can look up in the standards to see what to expect. The process is the same worldwide. On the minus side, you have some hoops to jump through, such as getting letters.
If you have insurance (including Canadians, Brits, and others who have government health care plans), the insurance may insist that you go to to WPATH-certified doctors or you won't be covered.
On the other hand, any doctor can write you a prescription if you can convince them, by pleading or by cash, to do so. They will insist that you sign an informed consent document just to cover themselves against lawsuits. This is called the informed consent model.