That really does highlight the massive differences even between regions of the UK. You'd barely get a micro down here for that money (45x8=£360).
What does an average house cost round your way?
The house might be a bit cheaper Doob, but food still costs the same, so does diesel and the machine itself. The reality is the margin is tight on that size machine unless you can get it working on something specialist, which if you think about it, is what most of us do on here. Plenty round us going out for £250/day with a 1.5t and no vat... but they aren't on this forum much - or at least don't seem to join. We on here seem to be a unique breed of people so interested in plant that we want to talk about it on the internet rather than do literally ANYTHING else of an evening - but it does lead to good knowledge sharing and ideas get bounced around, some of which no doubt go on to earn that person more than the next man. And rightly so, you put the effort it and it should get rewarded.
Thing with a 13t is it will do a lot more £45/hr's than our minis will before it needs replacing, but it also has higher running costs and the depreciation is greater... I hired a guy in 2020 with a 14t and tiltrotator with all the attachments and Idig for £350/day+vat including fuel! Bloody good value if you ask me - I have no problem paying that invoice, you should see the work he got done with it in a week - I was £££'s in!
But if you don't want to get involved in all the stuff we do outside of actually driving a machine, then I guess you are left competing against the rest of the market which is very competitive.
As for the OP's predicament, its sad that they took this view, but it is on you as the supplier of goods to set the price before the transaction. Even if you add it to your T's&C's that any extra over work above the priced work is at £x/hr, then if this situation occurs again, you have something in writing previously agreed by the client that goes in your favour. I know how it is, the work rushes ahead, you mean to have the conversation with the client but they arent on site or its an awkward time, and before you know it the works done and its invoice time. I've been there - many of us have! You pay to learn they say

Key is not to make the mistake a 2nd time.... I've done that too...