You're probably right. But people do do it .
On the thread I referenced, a couple of posters said that yes, they couldn't apply for passports or driving licenses and had had to make their peace with that they would always have to remain in the UK and get cash in hand jobs and the like.
Other people have already said about the ' mum uniform' of puffa coat, jeans, boots etc. I see hundreds of women a day wearing exactly that. I couldn't tell half of them apart. If she's in a major metropolitan area, she just needs to stay out of sight for a month or so and people will have forgotten what she looks like.
I've been following this story for a week now and am not confident I would notice her in the street if she was wearing different clothes/ had dyed or cut her hair. We all like to think we would, but most people are fundamentally unobservant.