Transfer US based Drupal websites to UK hosting

I have 2 websites on the same hosting package at hostgator.com in the US. Both websites have been designed using Drupal, PHP, MySQL. The domains are registered at 123-reg.com so we have control over the DNS and nameservers and wish to transfer the websites off the US hosting and onto a UK based host. The host can be of your choice but must be reputable well known company with excellent speed and automated backup.