Although immigration increases economic growth and healthcare relies on workers from abroad. (Although that is really legal migration and you are talking about the 30k of illegal immigration that is tiny, if any, impact on economy of UK.)
That’s barely half the story.
High volume immigration of uneducated and unskilled migrants has increased nominal GDP whilst leaving GDP per capita and real wages depressed. So there may have been growth but the British people have not benefitted for it. This is the macro story of the last 20-25 years.
Illegal immigration is higher than 30k, that doesn’t even cover the small boat arrivals which are about 45k, visa overstayers exceedsthat (50-100,000/year). Reasonable estimates put the total undocumented population of the UK to be 800k+, this is not a “tiny impact”.
The waters are muddied further (on purpose i believe to obfuscate the headline numbers) by excluding many people who enter illegally who are “legalised” through the asylum process.
Yes, some sectors like healthcare are heavily dependent on migrant labour and I’m all for importing skills we actively need. But the majority of people entering our country, legally or illegally, are not in that category.