Welcome to the forums!
Unfortunately, it's not perfectly straightforward. For example, AV UK currently uses a UK database and I've noticed recently it is indexing sites faster than the AV.com
It will accept .com and .uk domains but I've noticed preference to returning better results for .co.uk records.
It really depends on whether the SE is trying to establish a .uk flavour to its records and you can identify this by doing a search for site in the uk engine first, then checking the .com engine for those records. Your own site may be a good start. Make sure you select the option to search either "uk only" or "world" or "web" or "internet" etc., as appropriate.
Again, depending on the engine, some uk SEs are filtering and rejecting submissions for .com domains.
As far as directories are concerned, if you are referring to Yahoo and you are listed through your submission to the .com directory then you should not resubmit to the .co directory, unless you have a uk-specific site and different site. The submission policies on each directory is a good place to look for further details.
Having purely a .co.uk domain will help you get into some of the directories/engines which reject anything other than uk/ireland-based sites.
Take a good look at Excite's results and its filtering.
Hope this helps!