The thing to remember is that the violent protestors are a tiny part of the British population. Also that their were just as many "Refugees welcome" protestors.
On the question of immigration, and as you say, we will always need some, but we currently have 10.3 million foreign-born people in a country of 68 million, which I think is way too many.
I too was a migrant, and worked for 3 years in Australia on a temporary residency visa. When applying for the visa the company that I was going to work for had to show that they had private medical insurance for me. What happens in the UK is that we have many millions entering the country who have the same rights to use the NHS as any Brit does. There are currently 7+ million on NHS waiting lists, and I reckon part of this is due to them having 10+ million more 'customers' than they would've had without mass-immigration.
If legal migrants in the UK were told that they had to get health insurance in order to get a work visa for themselves and their families they might decide to look for work somewhere else instead.