@WWYDwiththisone you say in your OP that "I don’t know where I stand on it legally", but that's not quite true as you were given some excellent advice on that thread.
To take your situation stage by stage, you say the cleaners were late arriving. I don't dispute that, and some people might take issue with it, others might not.
However, apart from this being an annoyance to you (and I totally get that), it is not at all relevant to your complaint, in as much as you're complaining about the quantity of work they did in the time they were on site. Had they arrived on time and stayed longer, you could well be now writing your mumsnet post to say "cleaners did five hours but I'm not happy with the work they did".
So for clarity, your complaint is about what you got from them in return for 3 of their man hours, for which you have been invoiced £69.
As I said on the other thread, I have spent two decades in the cleaning industry, mostly running my own domestic cleaning service, but have also worked as a consultant to the industry, freelance, carrying out other services for other organisations, such as training, lecturing, and conflict resolution between clients and cleaning businesses.
When you booked these cleaners, it was agreed that you'd be paying by the hour. You also indicated what you wanted doing, but the fact is you knew you'd be paying for their time and not the outcome. You also said that the time they would be onsite was not capped either.
Similarly, the cleaning company has not showered itself in glory either, and they sound either very new to running a cleaning service, or else are not very efficient at it. They absolutely should have done a site visit and evaluation (either before the day of the clean or at the very, very least before they started any cleaning, and for that I put full responsibility on them.
However, you are not disputing the time spent onsite, you are disputing what you got for your money. And again as said on your other thread, without seeing the condition of the fixtures they cleaned, and knowing what chaos they had to work around, no one who wasn't there can comment accurately.
But still, it all circles back to the same thing - you agreed to pay them for their time and not for the quality of their work. They have sent you the invoice accordingly.
You have told them you don't think it is worth the money they are charging, they have responded by saying yes it is and we'll be charging a late payment fee too if you're not careful.
That last part gives you a massive insight into the type of people you are dealing with (it's incredibly crass IMO), and for the sake of your own sanity and to be able to carry on with the rest of your life, my advice was to pay it and forget all about it. Don't complain, do not review them, and do not antagonise them further. You do not need this negativity in your life.
But it was only advice after all, and you are free to ignore it, which you have. That is your absolute right. You have decided you should pay them less, but you've no idea what to pay them - and if you don't know what it was worth, how can we? You can't say "well a few hundred mumsnet users voted i was not being unreasonable based solely on what I wrote, so clearly I'm right", I mean I feel ridiculous just typing it. The onus is very much on you to prove that they didn't deliver, and once again we're back to the same point, they are charging for their time, not their quality.
They do not sound the least bit professional, but never the less they came and they worked, and now they are asking to be paid for that time.
And all of this because you think that what you got is worth about £15-20 less than they what they are asking for. Fair enough if you are absolutely dependent on that money, but you have to ask yourself if it's worth it for the on-going problems you will be facing from them, because they aren't going to take it quietly - based on all you said about them (right from the start where they told you they'd got their childcare sorted; I mean, like that's any concern of yours, it's just crass) they are not used to being professional when it suits them not to be.