It's closely related to the paeleo diet many people rave about and of course, it's a life-saver for people with Crohn's and other out and out allergies. But the theory is that wheat is a recent addition to our diet and in the last 50 years we've completely messed with it. 4ft golden fields are replaced with 2ft unrecognisably modified varieties.

I didn't suffer from any obvious allergies, but still, stopped eating wheat and lost 8 pounds, have to remember to eat sometimes and don't suffer from the "afternoon blahs" any more. Also, I've not had that nagging black mood that sometimes descended. Two other friends have done it and one has lost a LOT of weight.

Anecdata. Which is why I just say give it a stab. It's also a relatively cheap option. Drop bread and pasta, add spuds and rice. (And read ingredients on processed food. Most soy sauce had wheat for example).

I think it falls within the OP's parameters of cheap.

And yes, one of the more strident advocate blogs screams woo.