Of course, this is all hypothetical because my kids and I aren't eligible for UK passports until Sept of 2005...and the first place I'm thinking of visiting on it is Cuba!
If you do travel to Cuba on a UK passport, and later on have to present that passport to a US authority, and they see that you've been in Cuba, you've committed an offense according to US law (it doesn't matter that you're a dual citizen and that you entered and left Cuba on the UK passport). You see, the offense is not limited to a US citizen entering Cuba with a US passport; the offense is that a US citizen enters Cuba at all.
Why would you need to give your UK passport to a US authority? When the Royal Mail lost my passport during my naturalisation process, I had to go to the US Embassy here in London to get a replacement. In order to prove I was who I was, I had to present...my UK passport, as I'm not a driver and have no other legally-recognised identification.
Now, all this being said, it's possible that Cuban immigration officials can stamp something other than your UK passport, thus leaving no evidence that you've been to Cuba. I'm unsure of this and a quick look at the Cuban Embassy website here in London doesn't give me any specific information. But do be cautious.
Yes, I know I'm a big wet blanket on this thread, always warning about stuff. However, better information is always good and I'm sure that travel to Cuba is possible on your UK passport with not much trouble.
Chris Hansen
http://www.hansenhome.demon.co.uk