For the LAPL, if you wish to fly any aircraft 'variant' which differs from the aircraft in which you took your Skill Test, you will need to have a logbook endorsement stating that relevant training has been given on the 'new' variant. Quite what that consists of will depend upon the difference between the variants, but should be proportionate. Clearly there is a lot more difference between flying a PA28-140C and a PA28-161 than there is between a -140C and a -140B and even more between a PA28 and a taildragger.
Some of this training would just require a cockpit brief; other training would require some flight instruction. But there's nothing specifically laid down.