First, understand that I don't accept the term "high levels of immigration" in the context of this debate. I consider it a pejorative term in keeping with the general tone of many of your contributions which have a "blame the immigrants" inference. I accept that you have repeatedly stated that you are not "blaming immigrants".
Immigration has supported our NHS workforce, significantly. An economy requires a healthy workforce so a direct benefit here.
Social care, including care of dependants (elderly and children). Without our immigrant workforce we would unlikely be able to provide the level of care in nursing homes, childcare facilities and other social care provision that we currently do. That responsibility would fall further on the family impacting on their ability to find work, most notably the women who have been enabled to become more active in the workplace over the last generation. One of the most significant reasons our workforce is growing is the fact that more women are able to work. Immigration has supported that.
The immigrant workforce contributes taxes and national insurance which in turn helps pay for pensions for our ever ageing population - if they were absent, the burden would fall even more so on the remaining workforce (including the low paid) possibly through tax increases.
Businesses have survived because of the immigrant workforce available to them, take that option away from them and they would fail putting people out of work.
On wages - the government's own report states there has been a "small negative impact on the wages of the low paid", this feeds into your narrative for sure but they go onto point out that there are insufficient resources targeted at enforcing existing regulations. " Inspection regimes are insufficiently robust and penalties too feeble. An employer can expect a visit from HMRC once every 250 years and a prosecution once in a million years." Which suggests that robust government intervention could address this issue.