I have a Sony A6000, which is quite old now but Sony have kept selling it alongside newer cameras as a lower price option. You can get one new for about £390 without a lens or £450 with the 16-50mm lens (try camerapricebuster.co.uk to find the best deals). The 16-50mm lens isn't greatly rated but it's probably worth £60 to get you started with the camera.
Then for other lenses I would go second hand from places like Wex Photographic, Park Cameras and MPB (or your local independent camera shop). The 24mm/1.8 (which Wex currently have examples of for around £400) is a fantastic sharp lens, great for low light situations, and the equivalent in field of view to a 35mm lens on a full frame camera, which is a good versatile length for street photography and landscape photography. Before that I used the 35/1.8 lens (50mm equivalent) a lot but I found it a bit too tight in many situations.
I've also got the Sony 18-135mm lens, which is versatile but as a travel zoom is obviously a trade off, versatility in one lens vs quality. The uncorrected RAW files show how much it relies on software correction. MPB have got one for £384.
The other option I might consider if I wanted to take photos in cities and the countryside is the 10-18mm wide angle zoom. I've seen mixed reviews, some people seem to get great lenses, others have faults, and for now I've stuck with using the wide angle zoom on my FF DSLR. Can be had for around £375 second hand.
Getting all three would take you well over your limit but I tend to buy a lens, get used to it, then buy another later.