You probably want somebody local to you.
If not: http://typophile.com/node/35023#comment-226163
Dislaimer: I don't own my own press*, I rent a Vandercook.
BTW my first generation business card** was light-on-dark,
which is pretty tricky - although it's a lot easier on nice and
dark black stock.

* Although I do own two sizes of Pascal.

** A (rather poor) photo here:
http://www.flickr.com/photos/48413419@N00/4121695105/in/set-721576228588...
An extra complication there was
that the ink was made using wine. :-)

hhp

The page you link to lists the design firms.

Here are a couple letterpress print shops:

Boxcar Press: boxcarpress.com

Cranky Pressman: http://www.crankypressman.com/cranky_pressman/

For these places, you are best designing your own graphics or hiring a graphic designer.

Also google "digital letterpress." Unless you want metal type, of course.

BTW, one of the cards on that page
went through a design crit here:
http://typophile.com/node/61540

hhp

As Hrant said, you'll undoubtedly want someone local (and as I see that you're in London, there ought to be many options), but I can highly recommend a local letterpress shop here in Seattle, Day Moon Press. They've finally got a website, though I don't think it represents them very well as yet:

http://www.daymoonpress.com/index.html

I've worked with Maura & Jack many times over quite a few years; they are not only skillful but imaginative, finding solutions that use the varying levels of technology to good effect. For anyone in or near Seattle, or for whom geographical proximity doesn't matter, I can't think of anyone I'd recommend more. (And yes, that *is* saying something.)