The wait for GICs is long, too long. Nonetheless you can help yourself. Take your diagnosis document and translate it yourself and ask your Finnish GP to sign the translation if he reads English. Translate your current prescription into English and get that countersigned too. Add the email addresses for the Doctors / Endos doing the signing.
Both Progynova and Cyproterone are available in the UK and both are used by UK services although most GICs prefer GnRH analogues for suppressing T. "Elleste Solo" is a suitable substitute for Progynova. Your UK GP will need to do blood tests and do your blood test 4 hours AFTER you take your hormone pills and look to achieve an E level of 400 to 600 pmol/L as that is what the GICs like to see.
When you get to the UK, you must register with a UK GP. Ask for the GIC referral but also explain your translated Finnish prescriptions and ask the GP to take over the prescription. GPs will prescribe if they can be convinced that you and your treatment are genuine.
Also, when you get to university, make an appointment with Student Health Services and show them your documentation. If the GP refuses to prescribe then Student Health Services might be able to help.
There is also the option of private Gender Clinics and there are two in London - TransHealth and GenderCare. Both charge about £200 for an initial appointment and (I think) about £80-ish for prescriptions.
Basically, if you make it as easy as possible for the UK GPs to verify your treatment then you are more likely to get the result you want.