I have been asked to quantify productivity gains following implementation of several initiatives to harmonise and standardise processes. What methods would you recommend for gathering and calculating this data?

When it comes to metrics associated with productivity related projects, I would always try to go with pre-existing KPIs for the processes affected. The first thing I would recommend, therefore, is to ask the people responsible for the processes how they measure their own work. The best thing, actually, is to do it in the early stages of the project. That helps all the stakeholders to understand what their trying to accomplish/impact. If the project is finished and there is no good enough response from the line of business, I would consider involving the D&A team to figure out a way to quantify the outcomes of the affected processes with the existing data, so that you one can compare the situation before and after the projects.

The simplest way would be to 
1. Document the process VSM before and after the implementation 
2. map each initiative with the process steps ( subprocess, activities ) where it is expected to improve productivity 
3. Compare the cycle time and output before and after implementation
4. Calculate the productivity gain due to the initiatives (that should be coming out of reduced operation process cycle time and increased output in the same time period.