Depends on the course and university, you would have to ask the admissions tutor for the course you want to do. I emailed loads of universities before applying and they were all very helpful in telling me what they would and would not accept. Each course gets thousands of applications so don't think for one minute that the head of that course sits and reads every personal statement and application, applications that don't meet entry requirements get filtered out before they get to anyone with any power.
Some people have got into university without meeting the general entrance requirements but I think they have had communication with the relevant person at the university before submitting their application. So if you are plannning to apply for a course for which you don't meet the entry requirements then email the admissions tutor for the course and put your case across.
The general enterance requirement are usually Maths and English GCSE at C or above or acceptable equivalent. If your Access course is accepted by the university it will meet the level 3 requirement. People may experience difficulty with the level 2 or GCSE requirement, as some universities are not keen on non GCSE English and Maths qualifications. But it is best to contact the admission tutor to clarify what is accepted.