The Labour government certainly did have a policy of shipping asylum seekers out of the Southeast into accommodation in places like Glasgow, Liverpool, and Birmingham. This was not compulsory, in that they could choose not to go - however the asylum seekers would then receive no rights to housing elsewhere. And since they were not allowed to work, the alternative was either find someone to put them up, or go underground and work illegally. What this meant was that single men would go off to pre-existing communities and disappear. However families with children would have no option but to go where sent. Coachloads of families turning up to condemned council flats in inner city Birmingham, Glasgow etc. Quite noticeable if you live next door! I know this happened because I witnessed it for four years.
Dispersal Policy
I don't really know what is happening since the EU accession, that was after my time working with migrants. However my limited observation is that EU migrants come to the country, work incredibly hard for a short time, then either integrate successfully and stay, or go home. I don't really see this as a problem - it's what has always happened.
There is a danger of conflating asylum seekers and economic migrants. They are completely different. I would also be wary of talking about 'Muslim immigration'. You may as well describe Eastern European economic migration as 'Christian immigration'. It would be just as inaccurate.