I’ve hired loads of skips over the years, some for my own DIY work, other through tradesmen. I have always pain an amount for the skip for a certain number of days, based on the size of the skip. I have never pain by the hour as original poster said, I think that might be a mistake.
The most recent skip was for a landscaping job, I was having a new drive with some fencing. I was given a meticulous quote, almost too detailed which outlined everything, materials, their labour, cost of skips etc and included info about unforeseen contingencies that would incur extra costs but it would be discussed with me first. As the work went on, the men found a sinkhole under part of the drive they were digging up which meant they needed to buy some more materials to fill it in. Then they discovered that some very large blocks of concrete, probably from an original wall, had been used as infill but they needed to be dug up and disposed of for my new drive to be installed. This meant an extra skip emptying was needed so I was given the cost for that. I’m glad I’d had such a detailed quote as it meant I could see exactly what the landscaper was going to do and where my funds were going.
I have never had a skip hired via a tradesman that was not filled by them. Neither have I ever had a job done where waste disposal was not mentioned before the work began. This landscaper seemed remiss and unprofessional for not giving you a written quote or contract and for not mentioning the situation re skips with you before you agreed to the work. Reputable tradesmen who need to use skips always get a better trade price from a regular supplier than I would be able to got for a one off hire.
In this case, you probably have no choice other than to sort out a skip yourself but could you ask the landscaper to move the waste into it for an additional cost?
It’s a bit of a nightmare for you at this late stage.
Good luck in sorting it out.