My username says it all.
One of the reasons for the level of migration to the U.K. is that the language of the U.K. is English (and Welsh in Wales) and the second language of the vast majority of citizens of other EU members is English.
Migration follows the language. For example, Italy and Spain have a lot of immigrants from Romania. It is estimated that there are about 800,000 Romanian immigrants in each - that's 1.6m Romanians altogether. Romanian is a romance language, like Spanish and Italian, and it is not that difficult for a Romanian to understand Spanish or Italian (more difficult the other way around because of the Slavic influences and vocabulary in Romanian).
The U.K. had a good argument that the language issue means that migration from the rest of the EU to the U.K. is likely to be higher than the other way round. It could have said that if in any six month period the net number of migrants from the rest of the EU exceeds a certain level no new National Insurance registrations will be accepted for EU migrants unless they provide (i) evidence of a degree-level qualification until the number of migrants in any six month period falls to below the specified level.
However, the U.K. would also have had to show that it was reducing non-EU migration - it's simply not tenable for it to complain about the level of EU migration when the net level of migration from outside the EU is higher (in some years twice as high) as from the EU.