One of the factors which led to the Brexit Vote was 'EU Free Movement', where voters perceived that unlimited numbers of Mainland Europeans could come to the UK to work. So why were UK Citizens not able to also benefit from Free Movement to a similar degree? Could the generally poor Foreign language skills of UK Citizens have contributed to this? Less than 25% of UK Citizens know a Foreign language well enough to work in the relevant Country, and it appears to correlate with the general observation that UK Citizens are more likely to visit mainland Europe for a holiday, or to live in a UK enclave, than for the Career or Business opportunities. I guess that this is academic now that the UK has already left, but if UK Citizens were as Multi-lingual as their Schengen Counterparts, then would the UK have been less likely to complain about Free Movement?
So why were UK Citizens not able to also benefit from Free Movement?
No reason at all. The issue was that few people wanted to work abroad, but lots of people saw an influx of foreign workers as a bad thing.
Could the generally poor Foreign language skills of UK Citizens have contributed to this?
It certainly doesn't help. Going to live in a country where you don't speak the language well is an intimidating business, unless you are joining an existing ex-pat community. However I suspect that economics plays a bigger role.
People move abroad for better jobs or pay. Few EU countries can offer this to English-speaking Brits. Most foreign workers coming to the UK are seasonal workers or have trades (e.g. plumber, bricklayer) which are international and have better pay here than their home countries. Since the UK has a higher per-capita income than most of the rest of the EU this doesn't work the other way around. (Interestingly, Eire is anglophone and has a much higher per-capita income than the UK, but I don't think many British are moving across the Irish sea. So maybe inertia has more to do with it.)
A bit more on languages
If you are a non-anglophone European considering learning a foreign language, or wondering which language to sign your children up for in school, then English is the obvious choice. Not only does it give you access to the entire anglophone world, but everyone else in the non-anglophone world is making the same choice. This means that if you learn English you can expect to communicate with people in many different countries, whereas if you learn, say, Italian you will only be able to communicate with people from Italy. (OK, Spanish is widely spoken in the Americas, and in some areas Chinese is important. But Europeans learning Chinese have a huge struggle).
On the other hand if you are a native English-speaker then the choice of 2nd language is much less obvious. Everyone else has already learned English (see above), so you are faced with long years of study to learn a language which might not actually help you; no point in spending a decade studying Spanish only to find that your dream job turns up in Germany.
Add to that the fact that most youth popular culture is primarily English (Hollywood, pop music, video games) and you have added incentive and immersion for non-anglophone children to pick up English which doesn't apply the other way around.
For this reason there is no real prospect of getting UK citizens to learn foreign languages.