While nothing stops you applying, I would agree with above posters about how your application may fare in light of the competition for both of those routes.
The other thing I always ask fresh grads who want to apply straight from undergrad is to consider what the impact may be on them (beyond the £30 application fee) to be rejected multiple times. People usually ignore this and say they will be fine, but to get 8 course rejections can have an impact on your mental health, especially when you are starting out and often feeling vulnerable and unsure of yourself and are likely to be facing many rejections in assistant psychologist and related roles.
I have been around long enough to see that the cycle of applications has an impact on people. It is a standing joke in my service that you can accurately gauge the mood of the assistant psychologists from the time of year it is. And realistically speaking it is also not just one year. There are threads on this forum about people who have applied for multiple cycles and get rejected year on year and are still no further. When I talk to 'unsuccessful' applicants (which is 77% of the people applying) it is the repeated rejections, the uncertainty and the sense they are waiting to be chosen which is the most painful part.
It goes against the "Go for it! You can do anything" spiel that is common on social media, but do ask yourself if you really want to subject yourself to this from now.