I think this is a key difference though. You initially asked about mass illegal immigration and I don't think anyone has ever been supportive of mass illegal immigration.
Is there too much immigration or is there just not enough effort to deal with them, integrate them once the government have approved their status?
The torys are very good at spin and propaganda. At least its easier to believe that than the majority of the country are that fucking stupid to believe anything they say without being deceived. If they wanted to deal with immigration, they absolutely could. Anyone who says otherwise might want to look at a map.
So rather than be angry with the people risking their lives to escape at worst or want to improve their life at best, look at the people in charge. May slashed border control forces before she was PM for example, police take a pay cut year on year if you take inflation into account, privatisation lead to all our money going into private foreign companies profits rather than back into the country...
The state of the country isn't due to immigration. It's an element for sure but it's not the root cause. You only need to see what the conservatives have done in the past 50 years to distribute the wealth as they saw fit and the working and middle class carry the consequences.
If you want to be angry, I don't blame you. But be angry at the right thing.