I posted this last week to someone asking the same...
What I will say first is £1000 really doesn't buy you a lot of car, especially now.
What I would possibly do is enquire through friends and family first if anyone has an old car they are selling, as you'd likely get a fairer price then and they are less likely to mislead you, even if it's just a daft wee C1 or Aygo to start off.
As above Gumtree, Auto Trader & Facebook have loads of cheap cars (You can't afford anything from an actual auto trader, only private sellers). As much as it may be your only choice, buying old/cheap cars as a new driver with little skills/tools from private sellers can be tricky, They often just want the car gone and don't mind lying or omitting things to get it gone and you have little way to challenge them after you've bought it. When you search cars 1000 and under, you start seeing a lot of 'Spares & Repairs', 'Non Runner' and 'MOT Fail' and the like, avoid all of these, you really want something with a decent 8-12 months of MOT left.
Depending on the make and model, a £1000 car will have a high chance of needing repairs soon, possibly expensive or near fatal ones, there's no getting away from that but there's good ones and bad ones. Ideally you want 1500/1750 to get a bit more choice, but you're still in the cheap end tbh.