I have checked 5 flights between London and Edinburgh.
All of them says Check in baggage 0 kgs, Cabin baggage 10 kgs.
Is this the case for every flight between these two places?
Nowadays many of the short-haul flights (and some of the long-haul flights) have a lowest fare that does not include any checked luggage.
This is usually shown quite prominently during booking (especially on the airline’s own website), with incentives to book more expensive fares which include checked-in luggage and/or other advantages, usually centred around flexibility (modifiable or refundable fares), number of frequent flyer miles earned, priority treatment, and so on.
You usually always have the option to add a checked-in luggage allowance to your booking, though: