Hi again Laura - I'll be social and write this message in English so everyone can see and add to it if they have any more ideas 😉
So, as I said I'm Dutch myself (23 years old) and moved to Leeds a little over a year ago. Looking back at it, the transition all went really smoothly for me so I'm hoping yours will be much the same! Obviously, make sure you have a few months' worth of supplies with you when you move over just in case of any roadblocks!
Then, what I did when I moved over first is find myself the nearest GP doctor's practice (huisartsenpraktijk). I registered with them and they applied for an NHS number for me (equivalent of the 'zorgverzekering', you don't pay for it but when you get a job you do pay part of your taxes towards it) and got me a medical exemption card. With that card you will get all your prescriptions for free (not just your diabetes supplies, but really ALL your prescriptions which is kinda nice!). They also made me an appointment to see the practice nurse there to take all your details and do a quick medical with you. I also saw one of the doctors, who then after a quick chat referred me to the nearest hospital to see the Diabetes Specialist Nurse (diabetesverpleegkundige). He also made a list of all the supplies I used at the time; test strips, lancets, insulin, needles (I was still on injections back then) etc and put them on a repeat prescription for me.
So, every time I need any supplies I hand in a repeat prescription and the everything is ready for me to pick up 2 days later from the nearest chemist. Do be careful about testing strips because in some areas they are trying to save money by making people use fewer testing strips. If they do, make sure you push to get the right amount that you need and don't settle for any less!
Also tell your GP about the kind of pump you use. They might be able to get the supplies for you there, or you might have to order the supplies through the hospital. Which hospital you get referred to MIGHT also depend on which pump you use (for example, my hospital can only fund Medtronic pumps and supplies so if I had an Animas one they might not be able to get me supplies for that and I might have to go to a hospital that does fund the Animas pump).
For me, all of this took only a few weeks to sort out but of course I don't know how things might be in London! Again, just be sure you have more than enough supplies with you. Your GP (huisarts) will be able to prescribe you the insulin so I expect your pumping supplies will most likely be the bits that take the longest to sort.
Hope this helped you a little! Again, if you do have any more questions or just want to have a (Dutch 😛) chat then don't hesitate to send me a message and I'd be more than happy to talk things through in more detail!
Best of luck with everything! Which Master are you thinking of doing?