Will the tradesmen take the old kitchen rubbish away

They are probably waiting on the skip company, it happens sometimes. Best thing to do is just remind them and I'm sure there will be a valid reason.

We normally hire a skip for the duration of the job and off hire it when works are completed, Id chase them up to see what's happening, If you don't have room for a skip they maybe arranging for a lift and load.

Try and contact him and ask him to update on about this.

Best thing is get in touch with the builder again and nicely ask him why he is not willing to take the rubbish away? If he agreed with customer to take rubbish away and charged for it that is his responsibility. It's not nice situation, but I am sure can be sorted

All depends on what's been set out in the quotation regarding waste removal, most of the time I store items neatly on site, preferably not on view and arrange for my regular, registered waste carrier to remove on completion.