tedster - 5:35 pm on Feb 9, 2012 (gmt 0) [edited by: tedster at 6:55 pm (utc) on Feb 13, 2012]
Google's intention is to sort this situation exactly as you described: the .co.uk should rank in the UK and the .com should rank elsewhere.
At various times they have some problems getting this right, but as a rule it does work as planned. I've never seen "duplicate content" problem with this set-up.
[edited by: tedster at 6:55 pm (utc) on Feb 13, 2012]