I don't think anybody objects to people who come here and pay their own way (in the same way as those who went to Germany in the 1980s did) sp.
What is objectionable is the fact that this country is importing labour to do unskilled low paid work and those who come to do it have their income supplemented by as much as 100% or more. They make no net contribution to the coffers - quite the opposite in fact - and on top of that their numbers place huge pressures on the health service, education and the housing stock.
The reciprocal arrangements you mention are not worth a light. Even if the vacancies were available UK people are not going to head off to Poland, Bulgaria, or even Spain, Greece or France because they will find that their income would be nothing like the levels they would enjoy here by doing low paid work and having their income topped up.
It is utter madness. If anyone can explain to me what benefit the country gains by supplementing migrant workers' incomes (much of which ends up being sent home and does not even benefit the UK by way of indirect taxation) whilst providing housing, education and health facilities for people who have not a hope in hell of being net contributors then I'd be willing to be swayed in my opinion.