Steve
We do that kind of work, possibly worse, for social services, but we don't take months, or even weeks. We would " gut " the property in two days, with a decent team of four.
The skips, to the best of my knowledge, should cost around £100, if they're actually needed.
All that's being done here, is a clearance. We usually have to carry out an environmental clean after removing the rubbish.
I would never price a job without seeing it first, but from the description and working as decribed above I would expect to charge around £1600 to clear the property.
Not sure about reason the kitchen units removal, that's just asking for trouble.