It is now a requirement that certain types of trusts, even if they are not taxable, such as a life interest in a property to a spouse type trust, are registered with HMRC.
HMRC have a Trust Registration Service Manual on their website which has full details of exemptions and requirements for registrations of trusts.
Trusts created by a Will
Co-ownership of property trusts
Examples of trusts from HMRC Trust Registration Service Manual:
What are the deadlines for trust registration?
Why do I need to register my trust?
What trusts are exempt from registration?
What information do I need to register the trust?
What trust changes must be recorded?