Erasmus is not homogenous, by any means.
In the UK, it probably did - especially in recent years - favour MC students, partly because the approach to MFL, especially in England, has meant that more MC children study MFL now that they are not an obligatory part of the curriculum. Also, the fact that UK MFL degrees include a year abroad meant that Erasmus mobility was geared more to those students than to others, though many non-MFL students also undertook Erasmus mobility.
But the UK also handled Erasmus in a specific way, as compared to France (I can't speak for other countries, but I've 15yrs experience of UK/France Erasmus mobility coordination).
Here in France, Erasmus is not a "semester/year abroad" - students study the full quota of credits and all grades obtained during mobility are converted and count towards their degree. Almost none of the UK universities we have exchanges with require students to take the full quota of credits while on mobility. Some ask for other work to be handed in to them. Some merely require students to spend a semester/year abroad.
There was nothing preventing the UK from setting up exchanges beyond the confines of the EU before Brexit and some do exist. But the funding isn't always equivalent to Erasmus grants, and visas and travel are more complex - so less privileged students have always been less likely to access those exchanges.
Now, the UK seems to be hoping that EU member states will continue to fund Erasmus and also pay to be part of the UK's very own Turing programme.
I've been fighting since the referendum to ensure that our students, many of whom want to teach English, will be able to carry on going to the UK to hone their language skills and gain the cultural insights and knowledge that make good language teachers. But my colleagues from non-MFL backgrounds think those students might just as well go to the NL/Belgium/wherever and take some courses taught in English. So I can't see them being keen to take part in Turing. And it's too late now for 2021-22 anyway. Also, takeup would be limited by the fact that the UK is now imposing student visas & integrated healthcare costs that mean most of our students simply can't afford to go to the UK.
I'll fight to try and keep the door open, but our university is chronically underfunded and understaffed and my fellow Erasmus tutors (all hard-working lecturers, whose careers do not benefit in any way from the long hours they put into ensuring these exchanges work - in fact, their careers suffer because those hours are not devoted to research and publications) are tired of defending the UK, and tired of the comments UK ministers and media have made about France and the EU. These are French academics who chose to devote their working lives to English Studies, who were all very attached to the UK and who are deeply distressed by the direction the country is going in.
These things are reciprocal. If we don't send outgoing students to the UK, my colleagues are not going to carry on dealing with incoming UK students. It's as simple and as mathematical as that.
Sorry for the long post. I knew that the UK would pull out of Erasmus, but that hasn't diminished my grief at seeing it happen.