I'm possibly repeating a few things here but there's been a lot of noise and daft suggestions so difficult for you to filter it all out.
Firstly you'll never get good braking with chromed steel rims, especially in the wet. And cheap long-reach brake calipers are rarely of a good design, so you're not going to achieve much, and it's not worth throwing money at this. Better brake blocks could help but only marginally.
Unless you have sentimental feelings for the bike, I advise you to sell it and get something with decent brakes. Any hybrid bike will have alloy rims that brake better, and most will have cantilever or V-brakes. You'll easily pick something up for around £50 on ebay if you know how to find a bargain.
As for the suggestions about retrofitting disk brakes, complete nonsense. The only good suggestion so far was to get cantilever brake bosses brazed onto the frame and fit V-brakes as they don't require any cable stops. You might be able to use your existing brake levers and even cables, but the cost of getting the bosses brazed on plus two pairs of V-brakes will be over £50 and it'll look messy with the resulting paint damage. So it's really best to replace the bike if decent braking is a concern.
You mentioned something about mudguards....that's irrelevant, you'll not be able to fit shorter reach calipers as it's dependant on the bolt to rim distance, which cannot be changed. The chromed steel rims really are your enemy here. And they're horribly heavy and slow as well.
Good luck.