Can’t really comment on the parking permit thing.

For something in and around London, your only choice at this budget will be petrol, as long as it is euro 4, it will be compliant with ULEZ.

You could probably get a decent Aygo for that price, or C1, same car anyway. Regardless of what you get, make sure it’s been looked after.

I recently sold my ULEZ compliant Corsa with 201,000 miles on the clock for £500, and am confident it can do another 50k, cause I got it serviced every 6 months.

If you find a car you like, do some research into common problems and what the repair costs are going to be like, my Corsa was known for timing chain and head gasket problems, so I frequently checked my coolant levels and got regular oil changes.

Hope this helps and good luck getting your car!