Thing is - these are now pre-existing conditions, are you looking at taking out insurance individually rather than with an existing company scheme*? If so that's not how insurance tends to work.
You could have course pay directly... like go for an initial consultation, pay for some tests, pay for a scan etc.. and follow up consultation. A consultation could be anything from like £100-£200 or so, you'd pay for any blood tests etc.. and an MRI could be like say £800 or something, then follow up consultation for another £100-£200.
Then depending on result you might want to get referred to the consultant's NHS dept.
If you're insured then your GP will write the referral for initial consultation pretty much no questions asked, much easier than they'd write an NHS referral. If you're paying yourself then you don't even need that, find the specialist you want to see and phone up their secretary and get booked in when they're next free. This can often be in a couple of days/next week etc.. unless you're after someone with a high profile who everyone with X disease has heard of and wants to see.
Some company schemes do cover pre-existing conditions and so you could just opt into yours perhaps if it does.
Also re: your 12 month wait - is that for your local hospital your GP practice always referee people to? You do realise you can be referred elsewhere (other teams at other NHS hospitals) if you request it.
