One reason the UK has a substantial skills shortage is because hordes of professionals are emigrating because of all the immigrants.
And the immigrants coming in are not, by and large, physics teachers or nuclear engineers.
Furthermore, when you lose all those professionals, you can't educate or mentor the current or next generation to fill the gaps.
I should add that I have nothing against immigrants per se - indeed, I now am one. It is just that the burden of taxation, reduction in services and quality of life deteriorate to the point where the UK simply isn't worth it anymore. Your average immigrant has to be not only a net contributor, but a higher contributor than the average member of your indigenous population (unless you have full employment, in which case they just have to be a net contributor). This simply isn't the case for the UK, and that's why so many the professionals are leaving.