Internal door locks?

[luca_01]

Hi all,

I'd like to be able to lock 3 internal doors in my flat, with keys.
The current setup is as in the pictures attached, the doors don't lock.

Would something like this work?

https://www.amazon.co.uk/gp/product/B004J3422G/

I guess I won't be able to use the old handles? I'd like to have a lever on rose handle as the existing along with a separate escutcheon for the keyhole.

Any advice is hugely appreciated as I am DIY newbie.
Thanks so much! Wishing you all a happy new year.

 

[mattylad]

Looking at the first 2 pics, those doors look like weak cheap doors and a good kick will open them no matter what locks you put on (even the hinges need attention).

 

[Wayners]

Put a mortice lock on. About £10.
Handles clamped with through bolts.

I'll find link

Edit.

Here is link

M3 Door Handle Fixing Screws and Sleeves, 30 Sets Door Handle Bolt Through Fixings Nickel Plated Connecting Screw for Doors Cabinet Drawers https://amzn.eu/d/hTTlLpY