Do you have WHM/CPanel on the current VPS? Because if so, there's no need to do any setup of DBs, email accounts or uploading the sites. WHM will copy everything including DBs and emails to the new server. The only risk that I can see of losing emails is during the few hours the DNS takes to change but I'm sure that eUKHost can advise about this.
If you don't currently have WHM then I can also recommend it if you do move - it makes life so much easier.
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