We have an excellent apprenticeship programme in place already where I work, training up maintenance and facilities engineers and the students are very good when they're done all have been given a permanent job and can go on to get very lucrative jobs in oil and gas, automotive, etc not our specialised type of business I am in. We also have very good training programmes both on and offsite, secondments, internships, summer students,company sponsored higher education, job rotations, etc - so more specialised roles like the biochemistry, electronics, mechanics, quality, finance, computer science, can all be trained for. It's a slow-hard slog though and you can't jump into these roles and start running and some folks may never get to the 'right skillsets' needed (as you have to maybe have to have a BSc/MSc/PhD in Electrochemistry or Mathematics or Statistics or Engineering or Biology). Which is exactly why companies have to hire folks on visas in the first place- they need people with skills and they need them 'NOW'-. It's how I got in- 6 years ago (its actually a very different industry now and there hasn't been in a while/isn't anyone new being sponsored for Tier 2 visas) - our company was really struggling to find people to fill the six open advertised positions, which had been open for months and months and months- they just couldn't find anyone with the "right" skill set. Only 3 of those 6 got filled, all of us on work permits. I am fortunate and blessed to be so lucky to be in the right place at the right time. In an economy now, I wouldn't be so lucky I don't think.
I whole heartedly support apprenticeship schemes and there should be more of them, give everyone a good foundation for their working lives - not everyone wants to have a PhD - not everyone wants to go to University -some folks have bills to pay, families to look after at a young age, they're carers, etc- so I'm all for training up in whatever ways and means possible. These programmes do work!
Likewise, like ksand24 says, there are a lot of things people train in that mean they actually have to emigrate - geology, archeology, oil, mining, Middle Eastern languages.... so just because they're trained, doesn't mean they'll stay put. Some of us have wanderlust!
It just seems like false economy to me to say that apprenticeships will mean that migration (both ways) will go away.
The problem IMHO begins in childhood. The UK (and the US) are simply no longer providing children with enough high quality science and math based courses. This leaves most teenagers ill equipped to make choices that would lead them into science and tech based careers. Putting an "apprentice" bandaid on it won't solve this fundamental problem.
This is why I am a STEM ambassador- trying to greatly encourage students to think about careers in Science, Technology, Engineering, or Maths and what they need to study now in order to do so!