Of course he could do something if he wanted to. He knows the law inside and out and could make the necessary changes to the law to deal with the problem. From my understanding Kier Starmer been very effective in changing the law in other situations!.
Illegal immigrants come here because they know they'll be housed, fed, clothed, given money and mobile phones, sent on trips to the theatre or the seaside ...They also know the law is soft on crime when it comes to illegal immigrants.
Kier Starmer could put a stop to this immediately if he wanted to, but he won't. He could use the military if he wanted to, but he won't.
Other countries have successfully managed to do something about illegal immigration so there's no reason why we can't.