A typical bath holds about 100 litres, so cold loft tanks are usually at least that big. It will not run out unless you use more than that, and it is not refilling, or it is refilling slower than you use it.
You can try filling a bucket under the shower, time it to full, calculate how many litres per minute it delivers. It might be, for example, 10lpm, meaning that you could have a 10-minute shower before the tank ran dry. If the tank is bigger than 100l it will take longer.
I think that most likely the ballcock stops filling when someone runs the kitchen cold (drinking water) tap, because that comes off the incoming watermain and is lower than the tank, so it steals all the flow. I do not think it stops filling when you run the hot taps or the cold bath tap., because, from your thumb test, I think they are fed from the tank.
The cause might be that you have an unusually small incoming waterpipe, perhaps a lead one that has been partly squashed flat; or it might be that someone has partially closed your internal or external stopcock, for example because they can't be bothered to repair a worn-out ballcock.