...they are presumably currently at least temporary EU citizens."
No they are not, jourdain. They are illegal immigrants who have no right of abode in any EU country. The problem is that having gained entry to the EU they are free (courtesy of the ridiculous Schengen agreement) to roam across mainland Europe as internal borders in that area have been abandoned. So you have the situation where migrants are "welcomed" into southern Italy (who have a programme called "Mare Nostrum" which is designed to rescue boatloads of migrants heading north from north Africa) and then quickly usher them across the border into France.
“If we opened the borders for a year, those who are law-abiding immigrants who did not qualify for Benefits in the UK or any EU Member State would die of starvation. “
No they would not, methyl. Those arriving here illegally do not die of starvation. They are provided with shelter (often in agreeable seaside hotels), food, pocket money and health checks. Unlike in France, they are not left to die on the streets. If we opened the border to such people (instead of forcing them to arrive here in shipping containers or contained within lorry cargoes) they would be treated no differently.
As tonyav has pointed out, Italy’s “Mare Nostrum” exercise is due to end shortly. However, do not hold your breath. There is no way on earth that they will allow boatloads of migrants to drown and there is also no way they will be towed back to north Africa.
The reason why Calais is inundated with foreigners is because they have been allowed free rein to roam across the continent after having gained (illegally) a foothold in Europe. Although the UK’s generous benefits system does not help, it is not our fault they are there. Italy should confine these people to their territory and either allow them to apply for asylum there (the first safe country they reach, as per the rules) or arrange for them to be shipped back whence they came.