Yeah, type-in traffic and everything else that goes with attaching your brand to the .com. Dot-com has become sort of a "metabrand". (The name of a business automatically gets attached to .com in a lot of people's minds.) Preventing a competitor from setting up there is a good idea too.
If that's your only goal, then redirecting it would work, for sure. Another possibility would be to launch a separate site there, but make that site *about* the .co.uk site. Once your brand starts developing, you'll want more than just the top 2 listings for the phrase "poker professor" in Google, and having a 2nd site at the .com where you write about running .co.uk is one way to get the additional listings. Reputation management, and all that.
You could even make it a
blog where any time you update the content on the .co.uk site, you post about the update there.
Anyway, those are just some ideas...