Occasionally when I'm driving with the cruise control on and hit a bump (sometimes running over road reflectors is enough to do it) my cruise control turns off just as it would if the brakes were applied. For some reason though when I go to resume or set a speed it won't turn back on, even if I turn it off then on.

I've found that putting my foot under the brake pedal and lifting up usually fixes it, so I'm assuming it might be a sensor or spring in the pedal.

Any thoughts?

Likely the usual suspect, brake light switch.
Ford's poor design (other makes do it the same way too) means the little switch has to bear the full contact current for all brake lamps (plus trailer if one towed).
Over time the small contacts get pitted, burned and get an arc residue on them causing erratic operation.
IIRC $15 for an aftermarket, 10 mins to fit using pointy nose pliers and a screwdriver. Take note of the way the rings etc come off when you disassemble.

The permanent fix is to fir a relay, fed from the hot side of the switch, contacting to the cold side.
Use a solid-state relay (ebay "SSR") to switch without a "click".

Buy a few switches while you're there, they'll become rare when they stop making them one day, and they do die often

Thanks mate, will do!

Is it possible to expand upon the relay idea? I haven't used solid state relays. Do they have the same variety of pole and throw as "regular" relays? And if so which one do I get?

SSR's are basically a polarised SPST. Wire it into the high side of the circuit, again they ARE polarity sensitive but that's easy enough, just keep the input and output's + terminals battery-side.
You can get them cheap on Ebay, bout $10 (eg {DESCRIPTION} ) Anything above 10A should be ok, 25A to be safe with trailers etc.

For $10 and half an hour's work you'll never change another friggin brake light switch again

Cheers heaps for the input mate, will definitely be giving this a crack

The cruise control has a vacuum switch on the brake pedal check it is square against the pedal otherwise and slight movement will disengage the cruise control. Should be a matter of gently pussing it in with pedal not depressed.

No worries, drop us a line if you need a hand with anything.

Moran:
The cruise controller uses the stoplamp circuit as the primary disengage signal.. that vacuum sensor is a safety backup and only activates under relatively firm brake application.
The pressure sensor isn't actually anywhere near the pedal, it's that solenoid-looking thing hanging off at right-angle, on the side of the master cylinder housing just behind the two hex plugs at the front of the whole housing.

It's a NC switch so easy to test but I've never heard of one giving trouble..

Prolly worth the OP testing this to make sure it isn't dodgy - just unclip the two-pin plug, stick a bit of wire in the terminals to short them out (don't let the wire contact the chassis, chuck a bit of tape over).
Drive for a day, see if it makes any difference. Plug her back in though or replace if fauly, you don't want an Aussie edition of the USA Ford Explorer locked-on-cruise saga