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« on: Wednesday 30 June 10 12:20 BST (UK) »
Came across your topic by chance and only last night watched a TV programme I'd recorded some time ago - it was the BBC's Who Do You Think You Are episode concerning Jeremy Paxman. It was a pretty old programme as I recorded it off some repeat channel.
His relatives were on Poor Relief in Suffolk until some time in the 1830s when this was replaced by the workhouses. To avoid going into the workhouse they joined a scheme which moved them from Suffolk to Lancashire (and eventually to Yorkshire) to work in the woollen mills. Apparently they were transported first to London then, by canal, to Lancashire and provided with jobs. Only children over 12 got jobs so this family left three younger children in Suffolk until they were able to be reunited some years later.
The scheme was run by Migration Agents and was paid for by the Poor Relief people. I'm sorry I don't know the actual name of the scheme.
My own relatives (being the contrary bunch we were) moved from Yorkshire to Norfolk so were opposite to the general flow.
Hope this might help solve your mystery.