Given the stakes (or to be more precise the lack of high enough stakes to justify hiring of a lawyer), it is perfectly reasonable for OP to self-represent at this matter. Everyone expects that. Some folks are making the path seem "fraught with danger" as if the wrong word said will cost them dearly. That's simply not true. OP's downside risk is only the £630 in play.
The way the English law works is, you bring every argument that is not patently unreasonable. When you are a pro-se litigant, the general practice of most courts is to be very forgiving on simple mistakes, like bringing an argument that is contradicted by a law you wouldn't know about.
No argument is perfect. Every argument has chinks, and those chinks can be identified and criticized by some oh-so-clever person from the Internet. It's fair to weigh that criticism. But don't get sucked in! Don't you dare become a shrinking violet afraid to raise a point because it isn't perfect enough. That timidity is a guaranteed lose. The system (especially toward pro-se litigants) requires that you raise every argument that makes sense. The system literally does not work if you don‘t.
There's an issue of timeliness. When the landlord accepted the rent checks as written, that's it - that's the rent accepted. If they didn't like that rent, they had an obligation to tell you the rent was short and that you need to make it up. That applied in October 2017. They were not timely providing you this notice in October 2017.
The argument I would make to the TDS is it's now too late. If you were paying too little rent, that means your rent was short every month from Oct 2017 to Aug 2018, getting shorter and shorter each month to where it became a significant fraction of the rent. And yet, they never noticed you of a single one of them. That defies belief; no reasonable landlord operates that way.
The landlord forgot about the increase, and that means both landlord and tenant agree the increase did not apply.