As a person who is a mature student applying as well for university,has received an offer and been rejected. I will give you my take on this.
Firstly the entry requirements for the course are generally the same as any other person applying, There are are alternatives ie as you mentioned Access to HE course.
As a mature student what comes into it is the grades you have , work experience /any additional qualifications (that you learnt later on , perhaps through work) that link to your desired course. Next your personal statement. Which is your chance to sell yourself as a mature student.
You will definitely have to apply through UCAS.
I want to study Chinese. I have a HSK level 4 in Chinese, studied in China twice. So I have a lot of experience and skill in the subject I wish to study. This is what I believe coupled with my statement and work experience that swung it for me.
So basically if you know you have no relevant quals, and or experience in whatever you desire to study I would most definitely look into a HE Course but enquire with the university you wish to attend what kind of HE course they are willing to accept. What I mean by this is if you want to study Science but do a HE course in philosophy ( if there is such a thing). That's probably not going to carry much weight.