We do, but we have a horrible imbalance in age. 19% of the population is past retirement age. That means over 11.4 million people in the UK are currently a drain on the UK financially. 17 million people in the UK are under 18. That leaves 38 million people caring for 28.4 million people.
Add to that that we as a country don't give a crap about caring industries (mental health, nursing, etc..) and don't pay enough for any right-minded indigenous person to want to do that work, and you have a nation that is totally reliant on outsourcing its care to people from other countries. And, as the pay is low, it has to be countries where the pay is low.
We haven't invested in the people of the UK for 15 years, so it isn't any surprise at all that we have become reliant on immigration.
That said, the one million figure for immigration does include 500k per year coming in for an education. This is both a great boost to the economy but also means many Universities are now very much tailored towards teaching the Chinese.
So, no, I don't think it is easy to change the way we do our visas. We need to change the way we think about social care and start spending money on the people who do it. Then we won't need the visas.