I've checked my local authority and they'll do it for £40 which is a ridiculous amount for one thing!
No it's not once you consider the costs. A truck which eats up a gallon of fuel per mile, an HGV driver and a loader and importantly the disposal costs and landfill taxes they have to pay.
I work in waste disposal for an LA, we pick up beds and mattresses and other bulky items for free but I wish we didn't. I don't believe the council should be responsible everything a resident fancies sprucing up their house. Our system is (IMO) abused to the point people are getting us to pick up small items like computer monitors they could easily stick in their boot and take to the dump themselves.
£40!!.....no wonder people just dump them on the street....
Which is why our management insist we pick them up for free. But the main reason in my experience is laziness not cost, we STILL get them dumped in the street despite offering a free collection service just because some people can't be bothered waiting the 10 day lead time we offer.
I've got a double mattress in a small hatch back before, just lay down the back seats and fold the mattress in half. Go to the dump, problem solved.