I am not claiming it is good in the long term but generally higher inflation leads to lower employment. At least that was the theory before the 70's.
I agree they did take jobs from the British mainly the young. However I do not think they are the driving force of the recession. You are right you can't have open borders and a welfare state.
We'll find out soon enough. The U.S. and U.K. are sure trying to prove you can. I always laugh at the "U.S. was built by immigrants" line. While largely true, the Irish, Chinese, etc. who came over in the 1800s didn't enjoy "free" medical services and other gov't goodies.