Hi, my name is James.
I cant see from the photos where the water is leaking from, however these type of issues are rather common.
Firstly you are correct this is a isolation valve which will shut off the water to the toilet, this type of valve only turns 90 degrees to close.
From what you have said you may have either over turned \ forced the valve beyond its limit and damaged the valve which means the water is likely leaking from the screw, if this is the case you need to replace the valve (this isnt a big job, but at the same time I wouldnt think this would be a chargeable if you speak to your Landlord and tell them you notice a leaking pipe.
If the water is leaking from the top or bottom of the valve where the compression nuts are (which is more likely), you just need to give the compression nuts one tenth of a turn with a spanner, as you may have rotated / moved the pipe\valve when trying to switch off the water, just turning the nut by a few mm should do the job.Please let me know where you think the water is comming from and if you require any further assistance.
Hi its been a few days since I had a response, I wanted to check if you still require assistance?
Hello I am just following up from last week, do you still require assistance?
No problem if its leaking from the screw its a sign the valve is starting to fail, you will probably find some lime scale has hardened around the minor washer you likely over compressed when trying to shut the water off.
It will probably be fine for many months, but start leaking over time or every time the toilet is used and the pressure in the pipe changes.
If you want to change it yourself (rather than notify the landlord) should it start leaking again, it would take a novice 30 minutes at most, have a look at the video here, it gives you the general idea of what is required.
To do this repair you ideally need two mole grips \ large pliers one holding the valve so it doesnt move the other unscrewing the nut, you can pick a pair up on ebay for £6. You will need a replacement valve which is about £4 from screwfix here, make sure you get the right size 15mm, I would also buy some PTFE tape which is about 50p from screwfix here. So all in all its going to cost about £10 including the tools.
The PTFE is only require if when you turn the water back on the valve starts to leak you wrap it around the compression two times and it helps with creating a water tight seal, the end of the video here probably explains it better than I am.
Please let me know if you need anything explained, appreciate if you can rate the service received so if not so I can close the case.