"What we do need is more encouragement/incentives for young people to go into the Sciences and Engineering."
Some actual facts would be more useful than the usual kneejerk responses about HE.
There are already large numbers of science and engineering graduates and by a large majority (sometimes up to 80%) they don't go into jobs in related fields, because the jobs are not there in this country in science and engineering (we invest far less in these sectors than many countries) and those science and engineering jobs that exist pay comparatively little, forcing science and engineering grads away from them. Ten or fifteen years of high-skill degree, Master's, doctorate and postdoc experience for a fixed term contract salary of 28-29k in the south-east where average house prices are over 350k and basic rents are over 1k/month anyone?
Whereas contrary to general opinion, broad liberal arts academic degrees tend to have pretty good employment rates afterwards.
Again, the target has never been 50% with a traditional undergraduate degree, and in any case that is a lot lower than the youth cohort percentage in our competitor countries, many of whom have better youth employment rates. The jobs aren't there for young people because those running the economy have designed them not to be, nothing to do with numbers of graduates.
The economic theories that have guided our economy over the last 40 years explicitly state that there should be a certain percentage of the unemployed, to keep labour values low, create labour market competition and force those who are employed to accept worse employment conditions than they otherwise would. The lack of "graduate" jobs is down to the way our economy is structured to push the cost of labour down. Look at the huge growth of internships (and workfare schemes, incidentally). If you can get "graduate" labour for free, and are encouraged to do so, why bother to pay?