Widening access does not increase you chances of receiving an offer per se, it only does so with respect to the relationship between your grade profile and the entry requirements of the course.
For example, suppose you achieved ABB. Had you not been a widening access applicant, you would not have met the standard entry requirement and so would be very unlikely to receive an offer. However, as a widening access participant you would have met the minimum entry requirement and so you application would be considered. (There's still no guarantee of an offer though.)
Similarly, if you (as a widening access applicant) exceed the minimum entry requirement by two grades (AAA) then you'd be much more likely to receive an offer that a non-widening access applicant who had the same grade profile (as they will have only met their entry requirements, not exceeded them).
Does that make sense?