A few points to consider..

1. Does the Tree Registry have jurisdiction over each of these trees?
I'm asking this because it's likely that individual champion trees are in a variety of locations, including public and private land. It's more likely that you'd need to get access permission from public land managers or private landowners to climb individual trees rather than from the Tree Registry.

2. Are there scientists active in Great Britain studying canopy biology and related ecosystems?
If you would like to get involved gathering research data it would make sense to contact scientists who are already working in this field and offer to assist them.

3. What is the source for the current measurements?
Is there a uniform system for the current measurements or are they coming from a variety of sources using different methods? The Tree Registry may not think there is a problem with the current measurements, or they may welcome your offer to provide more accurate measurement, it could go either way. If you haven't done this already I'd take a close look at current ground-_base_d and tree-_base_d measuring techniques so you can be prepared to discuss measuring options and suggest improved techniques if outdated or inaccurate techniques have been used to determine champion trees.

In the U.S. the Eastern Native Tree Society has published high-quality information about tree measuring techniques:
ENTS measuring guidelines

-moss