Russell. T. Davies is interviewed today by sci-fi's very own sci-fi wire, and he uses the opportunity to talk about Torchwood :
"We start filming in May, and we should be on in this country [England] in October," Davies said in an interview. "So we'll have two shows running simultaneously, which will be fun."
This corrosponds with yesturday's news, that production begings April 23rd (although I'd now guess this was more likely to be rehearsals for the actual cast than any specific filming). One 'source' on OutpostGallifrey recently let slip that filming begins May 1st, but whether you take this story with one big fat lump of salt is entirely up to you. One thing is for sure though: The media are going to go crazy over this series, just like they did for Doctor Who. And torchwoodtv will be there to record every moment of it.