Slight Grinding rattle when cold in the morning.

Hi guys.

Cars not being particularly nice to me, just got it back from the garage for a broken radiator fan (yay) and I've noticed something odd.

In the mornings, on the first few accelerations (out of my drive then accelerating down the road) I can hear a very slight metallic scraping/ squealing/ rattle. It's hard to know the exact noise. It doesn't sound belt-y But it goes away within seconds and I never hear it again all day.  This also isn't every day, and only seems to be after rain/ standing for a few days and on my drive which is a bit of a hill. At my partner's (flat) I set off with no such sounds.  When I set off from a car park after going to the store etc, I never hear anything.  It's literally only in the morning/ first set off.

Am I right in assuming it's the brakes being a little stiff to wake up? They've been checked through as there's often a metallic sound, but all was deemed fine but the drums are rusty.

Thanks