Alison - it can be fairly straightforward although the forms and terminology will not be so familiar for many trying to do this themselves.
Our PG 1 explains what is required re an application to voluntarily register the property for the first time -
Practice guide 1: first registrations - GOV.UK
If they bought in joint names then a certified copy of your Uncle's death certificate should also be lodged. Probate is not required as the legal ownership has passed to your Aunt.
The joint tenants/tenants in common you refer to relates to their beneficial ownerships and whilst important to check the conveyance from the 1960s and or wills etc since it does not mean Probate is required.
I would recommend reading PG1 and looking at form FR1 before deciding whether to do this yourselves.