I've paid £500 for a child's assessment, but I think it could be cheaper for an adult assessment as it will be more straightforward cognitive tests and less likely to involved discussions with teachers and parents. Perhaps £2-300?
I know that the Access to Learning fund in my university would fund a dyslexia assessment but you could only access that once you'd enrolled, so you are right, it might be worth paying for it now to get the wheels in motion.
If you get a dyslexia diagnosis, you can apply for a Disabled Students' Allowance before you enrol. This would involved getting a needs assessment and you'd need the EP report before getting that. And then after the needs assessment, you need to get your funding in place and liaise with the suppliers to get any equipment. It takes a bit of time for all the paperwork to go through as well - I think that if you wait until the start of term, you would probably be waiting until December to get everything sorted.
What you could get depends on your diagnosis and course, but it could include: computer with software, better access to library books, photocopying allowance, printer, scanner, dictaphone, pda, notetaker, extra time in exams.