Jules, a couple of q's:
What shoes do you wear when riding? Are they just runners, or actual bike shoes? If they are bike shoes, what brand/model are they?
I wasn't sure whether you said this, but are you using toe straps, normal pedals or clipless ones?
The problem could be due to a number of things. It could just be that your feet need a rest everynow and then, so do what Shell & John suggested by taking a break.
Your feet could be cramping for a number of reasons. It could just be that you are dehydrated - do any other muscles cramp at all? It also could be that your shoes are too tight, which would restrict flow to your feet, causing them to cramp. If you use toe-straps, they could also be too tight.
You may also just be putting too much strain on your tendons/ligaments in your feet. This would probably be solved by getting some shoes/insoles that have more arch support and a stiffer sole.
However, try the easy (and cheap) solutions such as loosening your shoes, drinking more and resting. It may be something simple. It could also be that your body is just not used to cycling longer distances (I'm not sure how much you ride, so can't be sure of this).
Hope this helps,