Hi Simon, I thought that since you already have experience with teaching at your university, getting some more money this way would be an easier route than finding money from elsewhere. I've never tried writing a begging letter to a company myself, but I would imagine that you're not likely to get a response unless it was in a company's direct interest to give you money....
....But maybe if there were some companies out there who would be interested in your research. Maybe having the contact with industry during your PhD would help your job prospects once you've finished...I'm just guessing here though! It would also depend on whether when you have finished, you would stay on within academia or whether you would be more interested to go to work in industry I suppose. I hope I've been helpful!