Recently BBC updated their app with the new Material theme, and it completely ruined the app, I reverted back to the previous version using Titanium backup, and I want to ignore BBC app updates indefinitely for now. Much like Windows ignore update etc. Is there a way to do so in the Play Store?
There is no such functionality in Play Store. However, some backup/restore applications, such as Titanium Backup (that you mentioned) as well as MyBackup support the ability to completely remove or break the Play Store link.