Are you saying the only way to deliver that prize is full relinquishing of EU membership? Or were there other ways that could have been seen to satisfy their underlying concerns that could have been tried first?
@lonelyplanetmum (sorry for delay in replying, I am travelling for work)
Why is low immigration a "prize"? Immigration rises when jobs are available for immigrants to do, because I think we will both agree that migration is primarily about people seeking new opportunities. If EU immigration goes down, then all things being equal, non-EU immigration will rise - which is exactly what is happening at the moment.
The way to reduce overall immigration is to make Britain less attractive, by trashing the economy and increasing unemployment. (You might decrease immigration in specific sectors, in the long term, by increasing training budgets but I doubt this makes a huge difference: UK population is ageing and not replacing retiring workers with new ones, it needs migration just to stand still).
Countries which want to control EU migration have some tools at their disposal, most of which the UK already uses, for eg by making it rather difficult to claim benefits (for both migrants and the native population). In addition, being horrible to EU migrants seems to be working quite well and the government has been - probably illegally in many cases - deporting homeless EU migrants for some time, by essentially criminalising not having a home.
But it's patently false to suggest that the 3 month rule is some sort of golden ticket to controlling EU migration, because most migrants plainly won't place an "exceptional burden" on the state even if they don't work (and most do work). The remain camp needs to stop chasing this unicorn.