Is it permitted to increase rent to cover communal cleaning?

If a landlord decided to draw up an agreement with a lodger, which specifically states that the rent will increase from x to y if and when weekly communal cleaning can be arranged, adding the month (say January) as the earliest date this might happen and also assuming the rent then remained at that level for the remainder of the six month term, would any such increase be a breach of the Tenancy Fees Act 2019 ? While I’m fairly sure, that even if it was allowed, it would have to be proportionate and require the lodger to agree in writing at least one month before any such increase, I’m not sure if the resident landlord would be allowed to do that cleaning ?

I think you’re complicating things. Firstly is this a resident landlord sharing some living accommodation with the lodger? If so then its a licence agreement that you will need. You need to be careful about what is written and I suggest you get a template from somewhere.

If I were you I would just set the rent to include whatever you calculate would be the cleaning costs from the start, then it doesn’t matter whether its you who does it or a cleaner.