The potential employer can ask the previous employer. The previous employer doesn't have to answer if they don't want to.
Many employers today ask potential employees, as a late step in the hiring process, to bring in a pay stub or two. If your colleague continues to lie, sooner or later she's going to get busted one way or the other, and either not get a job she wants or get fired soon after starting.
Oops, the above answer is US and since you refer to P45's, you aren't in the US. I don't know what the law is elsewhere, but logically there should be something similar or anyone could just lie.