They sound a bit like the father & son team who trim my hedges (so the council don't keep sending me those nasty letters about it obstructing the footpath) every now and then. They always start out by suggesting a ridiculous figure and we then spend a bit of time working down from there. After they've done the main job (admittedly always in a first class manner), they're always quick to spot something else that 'needs doing' and we start haggling all over again. Sometimes, after they've gone, I get annoyed with myself for not holding out for longer (e.g. when I realise that I've paid £100 for 15 minutes work) but at other times I feel quite proud of myself for knocking them down to a really low price. (They suggested over a hundred quid for a 'little extra job' recently and I got them down to £40 for something that ended up taking them a lot longer than I think they thought it would!). I quite enjoy the challenge of dealing with them!
Give this firm a try though:
https://www.anyjunk.co.uk/
They use licensed waste carriers all over the country, offering a variety of services (such as 'man with a van' and skip hire) to meet different needs. They're well-established and generally well-reviewed (although, like any firm that outsources work - such as courier companies - there are always a few dissatified customers).