Hello everyone.

I recently bought a 160k miles Octavia Mk2 facelift. The car seems in good shape overall however I have this problem of breaks squeaking (whistling?) a lot in low speeds. 

It's worse in the morning and much worse in rainy days. I think it comes from the rear brakes, slightly pulling the handbrake while the car is rolling gives a constant whistle. 
There's no squeak in high speeds, and after I go on a longer trip (60 miles) the squeak is completely absent after that for the whole day. Then the next morning it starts again. 

What do you think could be the issue? Maybe a break pad change? I noticed there's a huge corrosive lip on the rear brakes compared to the fronts. Do you think that could be the issue? I'll attach some images.
Thanks in advance to everyone.

Clearly there is an issue, if you're not au fait with brakes don't ask here, take it to a garage.

That rusty lip will come off quite easily if you hit it right round the disk with a hammer.  Just keep chipping it on the front and rear face along the outer edge until its off.

Wear safety glasses and a mask as the rusty bits will ping off and there will be brake dust.

Its an easy, quick job.

 

I'm not a big fan of Fatbloke's approach: firstly, I'd rather spin the wheel and use that to to run the rust against a chisel or screwdriver to get rid of the rust, secondly I don't think it will work.

 

I don't think it will work because I think the problem is that the brakes are sticking on, slightly. At least that's what it has been anytime I've had this kind of problem.

 

Now this can be a problem with the callipers being clogged with dust, which is curable with a hammer (use a bit of wood to transfer the blow from the hammer to the calliper, knock so some dust comes out, remove, repeat), or it can be a more serious problem, which may need a new calliper, although it may also be curable with a bit of lubrication (caution is advised, you'd have to disassemble things and use a specialist brake lube).

 

Or it could be the handbrake cable sticking.

 

Jacking a wheel up, and seeing whether the wheel spins freely should give you a clue.

 

Removing the dust; you are often advised to use a wire brush, but I am bigger fan of a clean domestic dustpan and brush, because then you are not going to damage the rubbers, as you might with the wire brush.

 

Oh, and this cure is likely to be short term, and may need repeating, say, at MoT time, which may make the new/recond caliper sound more attractive.

 

This kind of problem does become common as cars age.

 

And Fatbloke's warnings about safety glasses and a mask are points that you should really adhere to, and brakes are a thing where, if you are in any doubt, get someone who knows their job to do it. 

Brakes need a service ? Check disc thickness as there is a minimum limit. Check pad thickness and spring clip condition. Assemble with anti squeal grease ( I use copper grease). If calliper piston partially seizing then a bit more involved but still DIY