A-Levels are harder than Access in terms of content. The problem with Access is that to max out on distinctions really only shows you're an AAA student (going off UCAS equiv, and really it's more BBB in terms of actual content).
There's plenty of reasons to be sceptical of the OPs chance of success - implying that Access is a worse preparation for university than A levels isn't one. You might know applicants that haven't been successful (and the particular set up of applications at Oxford makes success with any 1 year qualification an extreme long shot - hence the crap acceptance rates) - but that's a flaw with Oxford's admissions process rather than with Access diplomas themselves. I'm sure they miss out on dozens of students who would thrive on their courses each year (you've probably known some)...but that's their loss.
Their access diploma would get them into Westminster without any other qualifications and Oxford only advise concurrent A levels to meet subject requirements. With 120 credits from the OU LLB the OP could well get into yr 2 at Westminster (compatability dependent obviously) and avoid them wasting an unecessary year studying A levels that aren't required for their backup choice and aren't recommended by their "dream" choice.