I think we've established that the girlfriend should front up and leave the UK asap. Does anyone have any different advice?
Nothing different to say from this end
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Just to add that in the situation described here, she's not an
overstayer in the way we use the word, but rather she's actually an
illegal entrant. It's a few steps up the ladder in terms of gravity.
When they refused her entry, they would have given her an IS98NW form explaining the conditions of temporary admission, and it lists out the address of where she is supposed to reside during that time. And if she's not at that address, she's got TWO problems. So if she leaves and the IS makes their house call and she's not there, then
he could draw an entry in the Sponsors Database. It's also their going-in assumption that she would have supported herself doing something illegal, like drugs or prostitution, which is an additional violation of the terms of temporary admission, although it is only implicit. Because if she tries to get an entry clearance in the future, the question will come up - that's for sure.
So when she leaves, it's a good idea to be accompanied through the port by an advisor whose objective is to assure all the bureaucratic bits and bobs are sorted. It doesn't help the situation, it just keeps things from getting immeasurably worse.
But that's optional. So nothing more to add M'lud...
I came back to add as an afterthought, that they don't usually book for drunk and disorderly unless there was violence or aggravation of some sort. rosscopecotrain, is there something about violence in your police record?