Most here highly rate the Sony RX100 as a general point and shoot. Have you looked at that? Do you just want something simple such as the above or something a bit more advanced?
I would look at some reviews of the Rx100, as they are very highly rated as far as image quality goes for such a small camera.
Perhaps have a read of this: http://www.whatdigitalcamera.com/roundup/camera-roundups/best-travel-compact-cameras-2015-464
http://www.whatdigitalcamera.com/roundup/camera-roundups/best-bridge-camera-2016-10525
This more what you're after?
I don't know much about bridge cameras I'm afraid, so reading would be your best bet unless someone else can offer some information!
A better/bigger/pricier camera won't automatically give you better pictures. I can guarantee if you stick me in a porsche, I'm still not gonna win any car races.
Do you have any requirements or preferences?
Eg Wifi, tilty-screen, weather sealed, OVF/EVF, big vs small, interchangeable lenses or fixed lens, touch screen, is weight a concern etc.
More advanced ?
Do you know how to go manual on a camera ?
That is what advanced means,the little sony Rx100 is an amazing little camera for the money,you will be hard pushed to find a better camera at this price.
You need to think about what you want to shoot, how you want to shoot, what gear you are willing to travel with and lug around, whether you want to be able to change lenses for specific photos, whether you see yourself taking tripods, flashes and extra else with you, or you want something that fits in a pocket etc. Are you going to spend time editing the photos when you get home or do you need good out of camera photos? Is your budget rigid or are you able to spend another 300-700 a year on new lenses, filters and accessories?
Camera size is really not important in determining image quality. However, your 500quid will go much further buying a 2nd hand DSLR and lens, but you will want to spend significantly more down the road on new lenses. There is also an important mindset, will you want to go out with 2-3 lenses and swap them over regularly depending on what you are shooting? Do you see yourself carrying a tripod around (if you really care about IQ then a tripod is a necessity for any static scene).
If you just want to take good photos without hassle or extra costs then something like the Panasonic LX7 is excellent.