I rent a ~50 year old terraced house in the UK, and had some plumbing work done recently. The plumber said the stopcock doesn't work, and so had to freeze the pipes to get the work done. This makes me nervous both for my own things and the insurance in case an accident should result in an unhindered flow of water. Is this something the owner is obliged to fix?
Your problem is not just that you don't have a working stopcock, but that you now know that you don't have one. Of course it's not illegal by itself, the problem is what is going to happen if you have an insurance case.
Your home insurance most likely has to pay for accidental damage. But any damage that would be caused by not being able to close the stopcock, when you knew it wasn't working, they could claim that this is due to gross negligence.
Whether they would succeed with that claim or not, I don't know, but fixing the stopcock seems to be a much, much cheaper solution.
PS. Seems I made a wrong assumption here - that it was your home, owned by you. The same reasons that would have made it a good idea for you to fix the stopcock obviously make it a good idea for the landlord as well. So I would make sure that you tell the landlord as soon as possible. If something goes wrong, and the insurance doesn't pay, your landlord would be responsible for the damage.
Whether it's legal to not fix the stopcock - that's a different matter. I thought you were the owner. You would have endangered yourself and your property. Nothing illegal with that. But with the landlord it's different; he wouldn't be endangering himself but someone else's property.