Hi.
I was getting some minor squeaking noise a number of weeks ago, so i got my brakes replaced [the front ones only needed replacing].
But I still get the squeaking noise, but slightly louder. And it usually happens when I haven't used the car in a few hours, or in the mornings.
And it only happens when I reverse.
I don't understand what it could be.

There's a few reasons why your brakes could be squealing. Where your pads bedded in properly? have the shims been put in properly?

I didn't actually fit the pads in myself. My step-father [ex diesel mech and toyota lover] fitted genuine toyota brakes for me [as he usually does]. He's fairly pedantic about doing things right when it comes to cars, so I would assume they were fitted in properly.

It is the same type of squeaking as it was making prior to the brakes being replaced, except it's slightly louder.

hmm, are the dics rotors glazed ? as in very shiny? if so requires machining.

If the rotor surface is glazed, get some sand paper and roughen the surface up... Pull the discs off and do both sides...

Roughen the pads up with the paper aswell and the noise will be gone...