Oh dear.. a Scot living in Yorkshire eh? ..bit like a Welshman with all the generosity beat out of him

All kidding aside..
I don't know the Dawes very well..but assuming it has rim brakes, I'd suggest, for absolutely minimal money spent that you replace the front cable inner (2 quid?) and lubricate the new inner well during installation. Also, check to be sure that your caliper moves freely and isn't bound up at all.
Next logical move would be new brake pads. Assuming you have something like standard shimano type brakes on there, you could grab a set of, for example the RavX Thermafoil brake inserts (roughly a 5'er) which are some of the best performing brake pads I've ever used (I'm 115kg and running them on my TT bike as a point of reference).
That combination of new cable inner with lube, and some new brake inserts will give you as much performance per pound spent as anything you're going to do.
When you do your front brakes, take a bit of time to properly center them in relation to the rim, adjust the pads so the face is perfectly parallel to the rim braking surface, and try to run the pads in as close as you can without any rubbing.
Lastly, clean the braking surface with a CLEAN cloth and rubbing alcohol or something similar, BEFORE letting the new pads contact the rim, so you don't contaminate them.
By the way, I liked those brake pads enough to do a mini review of them on my blog site:
http://anotherdooratthe.endoftheinternet.org/2011/06/09/ravx-thermafoil-3-function-brake-blocks-inserts-5-minute-review/Good luck sorting your brakes out.