"...destined for the tip when the dustman arrives on Friday."
Like I have said before, these language things fascinate me for no particular reason. I was able to figure out what you meant, although that would never be said using the same English language spoken words here. Over here, there is what's known as a "tipping fee" to haul trash to the local disposal site. In our case, we incinerate it and either use the steam to make car tires, or recycle odd pieces, or landfill degradables. In either case, the charges are called tipping fees. "Dustman" however, was a new one. I had to think about it a minute. Oh yeah; they must have regular trash route pickup days in the U.K. too... so trash day for Jazzy is Friday. We call that garbage day here. Mine is on Wednesdays, but I never ever use my local trash pickup... if I were to toss a bag of trash in my can, I may as well toss it in the woods, because a bear will come and get it out of the can if I do. The local bears here have adapted to know the pickup schedule, so on Tuesday night after everyone goes to bed, they tip every can in the neighborhood. Except mine. Sometimes they still check it to make sure. Nope, nothing to eat in there. (I carry all mine to a dumpster at work)
So dustman = trash truck driver.
And tip = dump, or throw something away.
FWIW - In my early days of public service, I was a dustman. On the day following Holidays, the little town I worked for would run an extra truck to catch up the missed days' route. The young guys in the Water Department were traditionally nominated to be honorary garabagemen/dustmen for a day!