Hi Paul - we can't tell you what's necessary or needed here as it's legal advice you need.
We register the legal ownership and trusts can often be set up through specific deeds or wills but they relate to the beneficial ownership so can, but not always, be reflected on the land register
It reads as if you have already started your own research on the topic so worth having a look at our PG 24 for guidance -
Practice guide 24: private trusts of land - GOV.UK
But please do seek legal advice as to how the trust has been created; what protection you all have; and how, if at all, you can/should or need to reflect it's existence and protect any beneficial interests on the land register