When turning a corner my rear wheel touches the brake pad, is this normal? I replaced my brake pads about a week ago and today I noticed that, when turning (or generally under lateral force), the rim touches one of the brake pads (depending on which way I'm turning.

I hadn't noticed it before but today was the first wet day so maybe the sound was louder because of this.

I don't notice myself slowing down at all, but don't really want to be unnecessarily wearing down my brakes.

The brakes aren't super close when released, maybe 2-3mm on each side.

I would expect a certain amount of flex in the wheel, but as I built the wheel myself I just wanted to check that this wasn't a problem with my build (though its already done 1000 miles probably so it cant be too bad!)

There would be room to widen the brakes slightly if this is all that might be required.

When stationary and holding the wheel and applying lateral force manually I can make the rim touch either brake pad without a great deal of effort.

Any input appreciated

Thanks!
You should check the wheel hubs. They may have too much free play. Take out the wheel and wiggle the axle. See Sheldon Brown's page here: http://sheldonbrown.com/cone-adjustment.html
The new brake pads may be closer to the rims than the old ones so that the fault showed up.