Jules, ....move to ????
That for me is not a question as it gives an obvious answer. The environs of Greater London have, at least for now, lower private rents and so will (for now) come under the caps.
Using your own example the £300 pw family of 3 with their £180pw to 'spend' on HB will move to the nearest place that £180 pw (£780 pcm) affords. So if Luton say has rents now at £700 pcm these will rise to £780. If Milton Keynes (slightly further north) has £650 pcm current PSL rents then these will rise to £780 over a short space of time etc.
In simple terms we see an ever increasing geographical circle around the capital that will see rents increasing to meet this cap.
Setting a "maximum cap rent" in government speak is the same as setting a "maximum target rent" for PSLs in my view and Im pretty sure they will see it this way.
Im not being pejorative here, but its the same principle and the same point I made when the initial £250 - £400 pw caps or maximum rents were first announced. PSLs in the provinces will look at this and say why are London rents 3 times provincial rents when cost of living s only 40% higher.
Setting a cap is a very dangerous thing to do as it also sets a "target" rent for rent maximisation purposes
This announcement has only hardened ny opinion on that.
However, the key aspect of this weeks announcement is the immediacy and inevitability that in the capital losing ones jobs means losing ones home with all the instability that will cause to the families involved.