Thank you! I still feel quite daunted, just not knowing what to ask for or where to look at the DIY store. I was worried about something like the holes collapsing into one another, or just not being able to get the drill into the corner even. I don't know if it's a hammer action drill. It's just a normal electric drill that I got at Homebase a while ago, nothing expensive. I don't know if it's plasterboard up there or not. I've never used plugs or properly drilled into the walls for anything, let alone the ceiling.
I could buy a masonry bit I guess, which sounds like it would cover me for whatever it might be made of. I've no idea what size though, or what screws or plugs even. I guess they'd have to be bigger than the ones currently in there, if those don't have plugs.
I will have a look at the colour if I can get the screws out, but that's quite hard at the moment, as it's currently a blind that goes across three windows, so very large, and I can't really lift it easily to put it back into place. I'm wanting to replace it with two smaller blinds instead, partly to make it easier. But until I know if I can put the brackets up myself, I don't want to order new blinds - it's a huge glass window onto the street so I have to be able to do it, and do it that day, if I take the old one off!! But the currently blind is big and heavy, and whatever the current screws are seem enough to hold it up, so they must be fairly secure.
I'd hire a handyman if I knew one, but I don't. Even someone just a bit taller who wouldn't have to balance on a chair to do it might find it easier, and even better if they actually knew about DIY. But at the same time, it shouldn't be that hard, I know...