You can use a 301 redirect to notify search engines and browsers that your site has permanently moved to a new location. You'll need to have both domain names pointing to your hosting while everyone takes note of these changes. It will take time for Google to update your listings and for returning visitors to see the change. If they have your site bookmarked, their bookmark will update automatically.
The following can be added to the .htaccess file in the root of your public html files. This will point any page at the old domain to the same location on the new domain.
<IfModule mod_rewrite.c>
RewriteEngine on
Options +FollowSymlinks
RewriteCond %{HTTP_HOST} ^olddomain\.co\.uk$ [OR]
RewriteCond %{HTTP_HOST} ^www\.olddomain\.co\.uk$
RewriteRule ^(.*)$ "http\:\/\/www\.newdomain\.co\.uk\/$1" [R=301,L]
</IfModule>
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