For any other Americans who were shocked British landlords could evict with 2 months' notice for any reason, I did some googling and it turns out section 21 _does not apply during your lease term_. It seems like a section 21-eligible lease in the UK is just like a US a month-to-month lease that requires 2 months' notice for the landlord to end. (For the Brits reading this unfamiliar with US leases, this is an eminently normal thing to have happen to a lease in the US at the end of its fixed term.)
Source: https://www.gov.uk/evicting-tenants/section-21-and-section-8... ("You cannot use a Section 21 notice if... the fixed term has not ended")