Just an update:
I am using CCleaner Pro v5.44.6577 and Kaspersky Internet Security 2019 on Win10 1803.
In my case, the crashes came first with this CCleaner version.
The workaround suggested by siliconman01 brought cleaning function back to work (Thanks for this hint!).
However, the browser monitoring process still doesn't stay resident in background; it is not loaded automatically when the PC is started up and it closes shortly after CCleaner is launched manually.
So, there is still an issue to resolve by Piriform ...
Regards, Henry04