The LL is solely responsible for paying their mortgage.
So, if the LL chooses a tenant on housing benefit, or lets an existing tenant stay, that should be the LL's decision, not the bank's.
https://www.theguardian.com/money/2018/oct/20/natwest-is-it-right-to-evict-a-woman-on-housing-benefit
'The tenant, a vulnerable woman, has for more than two years always paid the £400-a-month rent on time.
....
[NatWest] ..."in its correspondence with Helena that
“the options available to you are to seek an alternative tenant or move your mortgage to another lender”
....
^Helena [the LL], to her great credit, has done the right thing:
she has refused to throw out her tenant and told NatWest to get lost, taking out a mortgage with a subsidiary of Lloyds instead.'^
She has also organised a petition:
"Call on the government to stop banks discriminating against welfare recipients"
https://petition.parliament.uk/petitions/230012