@digmorcrusher and @AdvancedSetup, thank you for your replies. Ironically, I was without broadband connection for a couple of weeks so couldn't get back on the forum earlier...
Anyway, back to the original issue - a couple of days ago I got my connection back so I deleted and re-installed Chrome. That took me from version 49.xxx to 50.0.26661.94 and it worked perfectly for a day, but yesterday the same problem with Chrome not starting due to ''Protection Against OS Security Bypass - Exploit ROP gadget attack blocked" came back.
I read through other threads, noticed people referring to some settings which should be unticked in MBAE, but couldn't find the original message referring to details, so I decided to delete Chrome, MBAM and MBAE. I run Piriform CCleaner to remove traces from the registry and reinstalled all three again. At the moment, Chrome is working fine and I hope it will last a bit longer this time. The setup I am using now is as follows:
Windows 8.1 (x64)
Chrome 50.0.2661.94 m (so the same as two days ago and the same default profile)
MBAM (free) 2.2.1.1043
MBAE (free)1.8.1.1196 (previous version was 1189)
Trusteer Rapport 3.5.1609.47 (which strangely works in Chrome this time)
I'm going to keep fingers crossed and hope it will now run as it should.
Thank you again for your help.