ISA share lending

I know share lending is on by default for invest accounts.

For isa accounts can are we able to lend out our shares in our own names and recoup part of the interest associated with the lend?

I don’t think that would be possible. On a platforms you do not hold share certificates in your name, but through a nominee. The nominee is not permitted to lend out shares. Here is a quote from the Guidance Notes for ISA Managers, in the section titled Share Lending.

10.57 “Lending” of this sort by a manager is not compatible with his or her duties as an ISA manager. The title to investments must be vested in the ISA manager or his or her nominee, or jointly in one of them and the investor, the share certificate must be held by the manager or as he or she may direct and, above all, the investments must be in the beneficial ownership of the investor. None of this is compatible with an arrangement under which the investments are sold to a third person and subsequently replaced by different investments of the same kind.