No, it's not possible to cook an egg with two cell phones. At least, not by using the method outlined on wymsey.co.uk. The instructions basically boil down to this: place an egg between two phones, use one phone to call the other, and then wait for radio signals to cook the egg. Wymsey notes that cooking time:

very much depends on the power output of your mobile phone. For instance, a pair of mobiles each with 2 Watts of transmitter output will take three minutes to boil a large free range egg. Check your user manual and remember that cooking time will be proportional to the inverse square of the output power for a given distance from egg to phone.

As I said, this method definitely won't work (though I wouldn't rule out there being some kind of MacGyver way to cook an egg involving highly polished cellphones and reflected sunlight). What should be noted, however, is that Wymsey never intended anyone to believe it would work. The instructions are a joke. A lot of sites (including, surprisingly, Boing Boing) don't seem to have realized this. (Isn't the name Wymsey a giveaway?) The Wymsey site (which chronicles the goings-on in the fictional village of Wymsey) was created by Charlie Ivermee back in 1998, and he wrote the egg article in 2000. In an interview with Gelf Magazine he explains why he wrote the article:

“It was 6 years ago but I seem to recall that there was a lot of concern about people's brains getting fried and being from a radio/electronics background I found it all rather silly. So I thought I'd add to the silliness.”