Apart from emailing your clients there isn't going to be an easy way of telling them a change of address.
Depending on how the domains are set up will effect what happens to the mail. If there is an MX (?) record on the aplace.co.uk domain then you may be able to change things so it points to teh anotherplace.com domain and emails still get through.
As for importing address list...dunno! You may have to export and import via 3rd party software - eg Lotus Notes - Excel - Tobit. Not knowing either how Lotus Notes or Tobit work its all a stab in the dark!