The 3 core is between the switches.
The 2 core plus earth in the downstairs switch goes to the downstairs light.
Ditto for the upstairs
OK that will allow one of the lights to be wired two way, either upstairs or down stairs, not both.
The grey cable now that was funny, downstairs the blue was connected to the loop terminal and the brown was connected to the red wire to the switch but upstairs it was the other way up, brown was in the loop terminal and the blue connected to the red wire to the switch
Sorry now I am loosing the thread a bit, what I think you are saying is the supply and return to switch is swapped but in real terms colours don't matter, they should all be brown, or at least should have brown sleeves on them, all wires to switches are normally line, so may be blue but unlikely neutral it will be line.
When I look at the way lights should be wired I don't see why the grey cable is there and it's just like ELFimpudence drawing so I've made it like that for now except we have 2 switches for downstairs and one stitch for upstairs.
It is better now as nothing can get stuck on we'll just have to remember to switch off when we go downstairs.
I tried to do Ericmarks circuit but I don't understand it and the wire colours are wrong.
Yes now it is clear that is wrong.
So moving forward select which light you want to be two way, and which will be worked by one switch only.
With the one switch only the two core and earth goes to Com (L1 new switch) and L1 (L2 new switch), with the switch to be two way the two core and earth goes to L1 (L2 new switch) and L2 (L3 new switch) and it will not actually work light with just that wire connected, it needs the three core and earth and with that one what ever wire goes to L2 (L3 new switch) must go to same terminal on the other switch. Does not matter red, yellow or blue as long as that colour goes to same terminal on both switches.
If you want two way switching for the other switch, either you need another three core and earth or you can use wireless switches,
this method allows you to use existing switch, but I would say
this method is better option, however both end up a bit expensive.
Look at the
Sonoff range that is likely a cheaper option, but warning, although you can get neutral less light switches, they will not work with all LED bulbs. With the standard bayonet bulb (BA22d) my Energenie neutral less light switches worked fine, also with a chandelier and multi E14 (screw thread) bulbs, had mild pulsing when used with GU10 and real nightmare with G9 bulbs, they at first would not switch off and had to add a load capacitor, and they some times start to pulse. The same problem is found with dimming switches. So any electronic switch which does not use a neutral can have problems with small LED bulbs. Old tungsten work without a problem.
So although possible, it can have problems. May be better to use a smart bulb instead?