I don't know what the prices are on these cameras in British pounds but I'm on the working assumption that you didn't put them on the list if they weren't in your price range.
I'm surprised you can find a 650D (is this sold as "new"?) Canon releases a new camera in this series just about every year. In the USA, the camera you see marketed as a 650D in Europe is marketed as a T4i in North America. But then Canon came out with the 700D (aka T5i). There was virtually no real meaningful difference between the two bodies... but there was a big difference between that and the previous year's entry body (the T3i / 600D). Consequently, Canon actually still markets the T3i / 600D, but dropped the T4i / 650D when they released the T5i / 700D.
The 650D and 700D have the same sensor and focus system as the 60D -- but the 60D is a mid-range body. As such, it gets some treatment that the other bodies don't get. The 60D actually has some weather sealing (it's not water proof). They put gaskets on body seams and o-rings on the dials to keep out moisture or sand... should you get caught in the rain (warning: the lens will not necessarily also be weather sealed and not every part of the 60D is weather sealed. You'll see the battery door and memory slot door do not have seals, but then the battery door is on the bottom of the camera and even the memory card door (on the side) place electronics far enough from that door that a moderate rain is probably not going to manage to get moisture to anywhere that matters.
The other thing about the 60D is that it has a control layout more like a pro level body (because it's a mid-range bodies and mid-range bodies get some pro-like treatment.) Notice the back of the 60D has a large dial in addition to the normal "main" dial located on the front. That's because when you shoot in manual mode, the front dial controls shutter, the back dial controls aperture... and if you shoot in a semi-auto mode, the front dial controls the main setting (either aperture or shutter depending on the mode) and the back dial controls exposure compensation. With entry bodies you only get one dial and the dial does one thing when you use it and something else if you press-and-hold a button while using it. This makes the 60D a bit easier to use. Lastly, there's also an LCD on the top of the 60D body with a number of extra buttons there. This display some camera settings and info and the extra buttons provide some instant access to frequently adjusted settings (e.g. chaining ISO settings is very common so this gets it's own button.)
You may wonder why a mid-range body is available for a price tag more similar to the entry-range bodies. That's because Canon introduced the 70D (the "new" mid-range body) and while the 60D is still available, it's price is lowered.
What's NOT different on the 60D is the sensor or image quality. That will be the same. The unique features of the 60D are all about the body layout and control and a few other body treatments. I used to say it has a better focus system except the most recent entry bodies now have focus systems on par with what the 60D has so that's no longer really a differentiator.
On the Nikon side, the D5k series body (D5300/D5200) will certainly be the more feature rich body than the D3k series body (that's their low-end entry range series). But on Nikon, the D7k series bodies are the mid-range.