You could easily get away with a front disc only since you should be using the front brake almost exclusively, at least while on decent surfaces.
You didn't mention what type of headset your bike has. I'm not sure if it's possible to do a conversion with a threaded/quill stem headset but it can be done quite cheaply with a standard threadless headset. Here's how I'd go about it assuming you're running 26" wheels. If you have 700c you can find comparable parts.
Finding a rigid 26" fork with disc brake mounts is a real pain. They do exist but are hard to actually buy anywhere in my experience. You can get a basic suspension fork like this one for £30. Just put on lots of preload and it will be comparable to a rigid fork and it has the all important disc mounts.
Next up is a wheel. I've had good experiences with cheap n cheerful ebay wheels so long as you check the state of the bearings when you buy - 99% chance they'll be too tight and without enough grease. Both easy fixes. Something like this wheel for £30 looks like a good deal. The only maintenance needed here is to repack the bearings maybe once a year. Doing that should make it last for a long time without rim wear to worry about.
Lastly the brake. My advice is to skip cable discs and go straight for hydraulics. I've used both and I'd never want to go back to cables. This mtb brake is an absolute steal for £30. I have an older version of this brake that's seen close to 2500 miles in all weathers on one set of pads. Has never needed a spot of maintenance and still stops as sharp as ever no matter what the conditions. They benefit from a bleeding once a year but you can get away with less - and it's only £15 or so at a bike shop.
So, with new parts, there's a disc brake conversion for a shade under £100. You can lop that price right down if you could find a secondhand fork for less (bikestation has a few I think) or a cheaper disc wheel etc.
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