Technically you could do that. However, you are staking a lot on things going to plan and that is in the context of Brexit and an impending global recession where there are going to be lots of graduates competing for those slots.
I can talk about my experiences as someone who manages clinical psychology staff, and have had several assistant psychologists (who have gone onto DClinPsys) and recent trainees work under me. You are going to be up against many very intelligent, highly motivated graduates who have local experience, connections who are in a place where they can work for free and/or live with families. They won't have to pay back expensive loans (as the Student Loan company waives repayments under a threshold), whereas you may be pressured to take on any job just to survive.
I have no idea who you are and your personal circumstances, but do be aware that this is more about a competition for limited places, than a question of "If I do A+B+C then I will get my desired outcome". It is a huge risk, especially if you don't come from money, but only you can make that decision.