We could do with Barmaid's help here but my own view is that the tenant is correct.
The Office of Fair Trading guidance states "It is unfair to impose excessive sanctions for a breach of contract. A term that requires the tenant to pay more in compensation for a breach than a reasonable pre-estimate of the loss caused to the landlord is likely to be void as a penalty under common law":
https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/284440/oft356.pdf
i.e. the penalty charge specified in the tenancy agreement should not be more than your costs involved in (say) sending a reminder letter, together with your (very small) loss of income through not being able to put the money into your bank and get interest on it. So even your original £25 penalty charge could be open to challenge as being excessive (and therefore invalid in law). Since you would not suffer any additional losses through a late rent payment after the second contract document has come into force, it's hard to see how any further charge could be held to be valid in law.