Rainynovember.
The very use of the word "uncontrolled immigration" is part of the problem, its a loaded term which brings to mind the same kind of images that were on UKIP posters.
Your points regarding funding, well its austerity which has been a policy of the Conservatives that has impacted most service elements, in fact falling immigration leads to lower tax revenues but doesn't have a corresponding fall in demand for services so services are less funded. Any arguments about the impact of immigration on services need to be tempered with the impact of austerity.
The point regarding impacts on the poor is true, the BOE found that a 10 percentage point increase in immigrants working in unskilled occupations leads to a 1.8 % decrease in wages for domestic worker.
Except we've never had a 10% percentage point increase in immigrants working in unskilled occupations, the highest we got was a 7% point increase between 2004 and 2006, further, the very poorest had this minor decrease offset by the increasing tax threshold from 2010.
I find the faux hand wringing for the poor a little bit much to take really, seeing as brexit and the inflation because of it will massively impact their spending power by more than immigration has.
I'd also question the whole "enough" rhetoric because areas of higher immigration invariably voted to remain whilst those with the lowest levels voted to leave.