Welcome to WP, Neil.
I was formally diagnosed, here in the Yorkshire, only a few months ago - so it's not so long ago that I was in the position that you are in now.
Your self-test scores are certainly indicative that an assessment is appropriate, and I would advise you to take those along to your GP appointment. Most GPs know very little about autism, and can be prone to applying the same stereotypes that others often do in everyday life. The self-tests are good evidence to have on hand, and are even used by assessment teams as part of the initial screening, so they do have some clinical merit that you can point out if your GP is sceptical.
Waiting times can, sadly, be rather long. My GP had to try twice to get my referral accepted due to "funding problems", so try not to be disheartened or give up if your first attempt is not successful. You also have a right, enshrined in NHS policy, to a second opinion if your GP is not co-operative. Once my referral was accepted, I waited about nine months before my first evaluation appointment, and the process then took place during five sessions spaced over a couple of months. However, note that this is extremely variable between different NHS trusts, though my experience seems about "average" from having discussed it with other people from across the UK.
In the meantime, you have come to the right place. There's no need for a formal diagnosis before getting to know yourself better and finding good advice from others who share your traits. In fact, although my formal diagnosis gave me peace of mind and has helped with "red tape", the understanding and advice from fellow autistic people has been far more valuable to me than anything that the professionals have taught me. I hope you find the same.
Best wishes.
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When you are fighting an invisible monster, first throw a bucket of paint over it.