What locks would you suggest for these doors?

[pollysproggle]

I need to keep my 3.5 year old out of a few of the upstairs bedrooms and the bathroom. I don't want to go back to the stair gate days as he's free to go up and down to his own room plus he'd probably climb it now.

It's a rented house, the door frames are not flush (see pic) but I want some sort of fairly strong catch or lock to keep the doors shut from the outside. Is there such a thing or a child proofing solution?

An ordinary cabin hook and eye would suffice but you should check with the LL first obviously, just to make sure there's no issue with adding fixings.

Thanks @TheNoodlesIncident
I always feel those hook and eye fixings are flimsy and with a good push they'd unhook?

Maybe I've only come across cheap ones before- I think I'll head to Homebase.
Yes landlord is very easy going about small fixings and the necessity of child proofing!