DavidR - Can you reply to my question as to whether I should let CCleaner scan Avast and then clean these items shown in my screenshot?
Personally I see little benefit in it as most of the .logs are for the benefit of the user and you lose that history. With the exception of the aswAR1.log the others are minuscule.
The aswAR1.log is created when you do a scan that includes the anti-rootkit module, so it will be recreated. When a scan is run with the anti-rootkit included (Full System or Custom scan) the resulting anti-rootkit data overwrites the existing file, so it shouldn't continually get bigger and bigger.
It effectively finds a level that is dependant on the data on your system, so for me it is pointless bothering to continually delete/clear these files.