If you're after a car on finance and that's the budget you may as well look at new superminis. Plenty to be had on PCP with a £1000 deposit and about £150pm payments. Granted you'd be looking at a petrol car but it'd be less trouble than a 4 year old car. Your mileage might be a bit of stumbling block - buying a used car outright would be best but I realise not always feasible.
You should look at manufacturer's websites to see what finance offers are to be had on their cars. Then look at autoebid or similar to get the lowest purchase price possible and apply the manufacturer offer (you will be able to do that in practice).
At the moment, for example, Mazda have a 0% PCP on the 2 (new 2 coming 2015). Supposing you got the 1.3 petrol (£30 tax, 56 official mpg) in a mid-high spec Tamura you'd be looking at £154/month over 42 months with a £800 deposit. Option to purchase for £3,445 after the 42 months. Only issue is mileage, you can either: 1. Pay more a month for that mileage, 2. Sell privately to make up the difference in the purchase option, 3. Save about £80/month to buy it outright so that your mileage doesn't matter.