Which countries practice this?
EU nationals can even vote in municipal politics in their new place of residence even if they're not citizens of that country; another big argument of the opposing party.
https://en.wikipedia.org/wiki/European_Single_Market#Free_mo...
1) You have a right to stay in another member state (host) for three months without any restrictions.
2) After three months, if you are not (self-)employed, restrictions can be placed on you. In particular, hosts will require you to prove sufficient resources to support yourself, including health insurance. If you are not employed and cannot prove sufficient means, you can be removed.
3) If you lose your job, you have a right to remain as a job seeker for six months. If you do not find a job within six months, you have to prove to the host that you are actively seeking a job, and that you have a realistic chance to get one. If you cannot prove that, you can be removed.
4) You get a right to permanent residence in the host after legally staying there for five years.
5) It is currently unclear if you have a right to the six months of job seeking before you've had an employment contract in the host state.
While I'm not a lawyer, I have used these rights myself three times now so I've read through them carefully as well as the local regulations in the countries I worked in.
[0]http://www.europarl.europa.eu/factsheets/en/sheet/41/free-mo...
Non-EEA nationals who are here long term just pay a surcharge for the right to use the NHS, but that's not allowed by the EU rules. In fact, the European Commission's position is that since the NHS is free, this rule should be interpreted as allowing everyone who comes here from other EU states to use it for free even if they're not working and not paying into the NHS, and that this should fulfil the insurance requirement.
There was a bunch of press controversy over the UK enforcing the rule as written in some cases a year or so back too.
Moreover the migrant worker has to pay tax in the country they're living in, so tax statement may be good enough.
Most of EU has "single payer, free at point of use" healthcare rather than US model of insurance.
And if they're not working, they can be elected after three months. Is three months slip enough to even put a dent in NHS budget? I'd say not at all. It's not like people are migrating to UK to get temporarily better healthcare. (It sucks compared to almost every other EU country.)
Additionally, for temporary stays, UK can probably demand reimbursement from the member country of origin.
