I think the clearest answer will be: you'll be lucky! Even the most inexpensive headshot provider is a working photographer of some description, and they all want to make a living! There are certainly cheaper rates delivered by some photographers than others; and a cheap rate is not always indicative of a drop in quality or a lack of experience, particularly because some great photographers offer cheaper packages in the hope of attracting maximum custom, so they feel they can afford to give you, say, £250 worth of shoot for £100 fee, which is always worth seeking out. But looking for a photographer who works for FREE?
Your best bet, if you really wish to try and spend no money at all on shots, is to try and track down a photographer who is in the formative stages of their career, and hoping to build a portfolio of work, in order that they can then go on to attract further custom, and appear in 'Contacts', on their website etc. as a serious professional. Because they have not yet set up in business properly, and know that their wares may not, therefore, always be trusted, they can offer the 'you scratch my back, and I'll scratch yours' option of allowing you a free shoot on condition they can use good shots of you for the sake of their own advertising. I have certainly come across this option before, though I don't know any leads specifically - your best bet may be to keep an eye on casting sites, like this one or Shooting People, where photographers of this sort advertise, and try and get in on a shoot for them. There are probably also photography directories of aspiring photographic artists online, and if you search through those, you may find some photographers who are still eager to bring in outside talent for free for the sake of generating portfolio work, although you'll have to a) search around and b) discover people who, however great their photographic talents, don't specialise in headshot work.
Certainly, you will not find any photographer in 'Contacts' who doesn't charge, and I wouldn't think any you could source from this site directory wouldn't charge, either - with that said, have you looked through the whole of CCP'S photographer directory to see if anyone is offering to work for free?