What's causing the noise from my brakes?

I have a 98 Honda Civic 1.6 LS, and a while ago it started to make an intermittent, high pitched, metallic squealing/screeching sound from the front of the vehicle. The sound would start after 5/10 minutes at higher speeds and stops immediately if I touch the brakes. It also seems to be slightly affected by steering i.e. If i turn the steering wheel one way it will stop and then back to straight or the other and it will start again. The braking seemed to be just as effective though. The sound appeared to be getting worse so I took it to a garage who said that a lip had formed on the brake disc that was causing the noise, so they replaced the discs and pads. I drove the car on the motorway that evening and the sound came back. (Interestingly it was raining on the way back and there was no noise).
I took the car back to the garage the next day and they said they took it on the motorway and couldn't hear anything. So I had it back, and it has been driving well for a few days, (all in wet weather, don't know if this has anything to do with it) but today has been dry and now the sound has started to return.
Any ideas? I'm pretty sure it's not a wheel bearing since it isn't that sort of rhythmic whirring sound. It also isn't the sound of wear indicators. Maybe sticking pistons on my caliper?

Cheap pads!

Some brake pads will "glaze" with brake dust and squeal like an old witch! Not all the time but enough to annoy you. If you turn the rotors or replace them, the new pads aren't as apt to be noisy, but may still do that. I still use the cheap pads myself because they seem to last longer.

When yours start making noise, go to the car wash and get the undercarriage wash as well, or use the hand wash yourself or even the garden hose and spray the brake area through the wheel slots. That washes the dust away. You may say that's crazy, but remember YOU mentioned the wet/dry issue!

New rotors (from Honda, not cheap Chinese knockoffs) and semi metallic pads will stop that, but cost about 4-5 hundred bucks!

Your rotors are scraping because your break pads are worn.