Hi Terris
Although i cant help you very much on the UK health system, i have moved many countries during time since my diagnosis in 2016 and ive never had an issue.
I have private worldwide insurance so i simply make an appointment with a hematologist-oncologist when i move to new city. They will take your history so i keep a record of important milestones ti tell my new doc like when i was diagnosed, whether it was chronic or advanced phase, wbc at diagnosis and when i went into full remission (ie when bcr/abl became undectable)
In the UK it will matter where you live and if you are going private or through NHS. There are many folks on here better versed with UK specific but aa far as changing countries, is gonna be fine. If possible bring 3-6 months of TKI with you so you dont need to stress about that when you first arrive.
As for stopping, uk docs are generally supportive but from personal experience, wait till you are well settled in your new country, i found stopping was more of a mental load than i was prepared for...