.co.uk was intended for use by UK based companies aiming at the UK market
.com was more intended for International Commercial companies.
However there never been any real control over this, and everyone and their dog can purchase them, this does mean that millions of these have been sold and it can be difficult to find a suitable name...
so there are other options you may wish to consider like:
.co
.uk.com
.me.uk plus more..
ps.. dogs must have owners consent before making a purchase -)