Sounds pretty unreasonable to me (residential property lawyer) so I would be considering the rent clauses in the lease carefully.
Have a read of UCTA 1977 as well
Hmm I don’t wish to snub your post but I suggest that the OP leaves it to his professional advisors to suggest a course of action based on the specific content of the lease and more substantiated facts, rather than pointing OP towards specific legislation which may or may not be helpful - it may lead to academic pondering and perhaps the OP misunderstanding his position, rather than achieving a resolution.
If I was the landlord, I would just counter any reference to UCTA by saying the lease wasn’t on standard terms (s.3) and, in any case, obligations regarding the payment of rent are expressly excluded from the provisions of UCTA as they are provisions that are integral to fixing the interest in land (sch1. Section 1(b)). At least, that’s the obvious counter-arguments. The application of UCTA would be massively dependent on the initial conclusion of the lease, with huge uncertainty re: the above exemption. So it’s not a ‘silver bullet’ for the OP, even if we found out that it was a lease agreed on standard terms.
Just wanted to mention that before OP wades in smugly waving “but UCTA!” in the landlord’s face
Normally, unless it’s completely black and white, it’s better to just reach pragmatic commercially focussed agreements and document them (using professional advice to understand the likely outcome of the dispute) rather than getting bogged down in winning legal arguments / disagreements.