If it isn't covered in thick dust then you really do need a different approach! Driving an issue resolution culture rather than grievances isn't all about having to change the policy, it's about a different philosophy.
Unfortunately, we have learned behaviour, which is to deal with employee issues through formal grievance processes. It's what HR professionals are taught at college, and it's what the increasingly litigious culture in the UK is driving - we have to go into defence mode and get the policy out so we stand the very best chance if this goes to tribunal.
Forget the tribunal or the formal grievance procedure - you can cross those bridges if you get to them - taking the right approach with people will mean you can leave the policy to gather more dust - that's a good thing!