For Cologne, a few places where you can watch games while eating. All have widescreens as far as I know.

Weinhaus Vogel ( Eigelstein 74 ): Traditional wine and beer hall close to the main station. Good German comfort food and safe wine list at very reasonable prices. Also nice mix of customers from every background. I'd recommend to watch at least one team Germany match here.

Gasthaus Essers ( Ottostrasse 72 ): Wonderful restaurant run by a German/Austrian couple and their friends. Mostly Austrian cooking with mediterranean touches and great wines. Only drawbacks are the 20 min taxi ride from the city center and dinner only policy. For me this is maybe the best restaurant in Cologne considering what you get for your money.

Restaurant Keule ( Heumarkt 56-58 ): Slightly upscale place serving German food and steaks in the old town. Both locals and tourists come for dinner or just a few beers or wine.

And for those England games:

Jameson Distillery Pub ( Friesenstrasse 30-40): Two big screens, hearty British fare, stout and cider and a friendly but football mad atmosphere.