Hey!
I know this reply is super-late, but I just thought I'd reply in case anyone reads this thread again in the future and wants to know. You can also get on the Hull doctorate by going to York for your undergraduate psychology course. They take about 50:50 people Hull:York, although the doctorate itself is in Hull.
You apply slightly differently - in your second year you hand in an application form (asking about grades and experience and why you're interested), they give you advanced modules in clinical psychology in your third year if you're chosen (usually 12 people chosen from about 20-30 applicants), then at the end of your third year you're interviewed properly to get on the course (only people who got on the modules are interviewed though).
If you're successful, you might be given a year out to spend getting experience or a job for a year within York Mental Health, with a promise of the doctorate to start the following year (i.e. you end up taking seven years to qualify instead of six). Sometimes people get on straight away so it only takes 6 years, but if you go through York, it more often takes 7 years. It's still competetive like if you were going straight throught Hull. However York ranks higher up than Hull on the league tables so if you're panicked about taking a risk by going to Hull but not getting on the course, it could be considered a better back-up to have a degree from there for when applying to other doctorates in the future.
Either way, both universities are great, and if you stick with it and do lots of experience and show passion for it then you'll get on a course somewhere eventually. Good luck! Feel free to message me for more information.