I don't think it's a problem. On land, you can use drones, walls and fences. On the sea, don't allow boats get into your territory.

In addition, there are many "soft" measures. Cooperation with countries like Lybia and Turkey. Help to alleviate the problems they are running from. Announce that anyone who crosses illegaly will not receive an asylum. Etc.

At the same time if you do nothing then you turn a sprinkle into a roaring river which is equally as hard and expensive to deal with.

The sheer number of people who keep moving after reaching France, Germany etc to try and get the UK, purely because they like the UK more, shows that choice and relatively small differences in final living conditions can have a dramatic effect.