Where to start... Yes there is a snobbery which isn't helped by plumbers calling themselves engineers. Plumbing is a perfectly honourable and well-paid profession. They don't engineer boilers although it could be argued that they have to engineer the networks that connect them to their clients (i.e. rads).
What's more pertinent is the fact that engineering and computing degrees are difficult and the prospects are entering an industry which is being decimated by bean counters who believe that those in IT just click buttons and whose jobs can be done by someone with loads of dubious qualifications from another country.
I don't think the education system has much to do with it. When I went to university back in the early 90s, schools' IT departments were barely functional and pupils were actively encouraged to not use the computers in case they broke them. Getting into an engineering degree wasn't too difficult. The degree was, however, and I can't help comparing myself with my wife who came out of uni with a good arts degree, having spent most of her time watching daytime TV, walked into a finance job and earns double what I do.
Why the hell anyone would want to get into the IT industry is beyond me. Until companies actually start going under because of the way their IT capability is being destroyed and people are held responsible for their actions then nothing is going to change.
As for the Brexit debate, this has absolutely nothing to do with it. It's the people in government here who are responsible. They're the ones being "lobbied" (the gentle western term for bribery) by big business to make sure short-term gain and bonuses are inflated at the expense of anyone and anything that gets in the way.