I was just thinking I wonder if they interpreted
as 18 pieces (6 times 3) but your invoice clears that up. If that had been the case, and assuming 30% overage on their side then they would have been supplying something like 12 cu.ft. making it a less-unreasonable £116/cu.ft. But they aren't, making it £220/cu.ft at the same overage (or £286 per finished cubic foot), which is very steep.
Item 1 - 6No legs which are 120x120 and 713 high (3 pieces to be laminated).
FWIW I gave a cut list like yours (finished dimensions) to actimber.co.uk near Ely last summer, and they charged me around £74/cu.ft inc. VAT for American Ash (measuring to the finished part dimensions, so ignoring both my wastage in milling the timber and cutting out any knots (there weren't many), and their overage in terms of available board sizes containing the sizes of my pieces). They picked out very nice straight boards for me and brought them all outside for me so I could load up the car. It wasn't a particularly large order – total including some other timber around £420.
I ended up with quite a bit spare too (maybe 20%?), so I think they allowed for me to discard more for knots/etc than I did (I left some minor ones in and filled them). This was on 1" sawn stock, which is normally a bit cheaper than the 2" you're needing for most of it. I milled the one inch sawn boards down to 21.5mm, so that's a 16% wastage right there. Together at a guesstimated 30% overage, that works out at £50 per cubic foot sawn lumber supplied.
(At the time I thought I was getting a bit of a naive hobbyist premium, but now I think I got a good deal!)
Edit to add: AC Timber didn't give me a price breakdown per board and just gave me a total, which was a strangely round number (£320 + VAT for the ash).
British Hardwoods do this too. "£323.44, call it £320 plus the dreaded..." working out the price per board means multiple calculations, and the rounding that I have had and seen has always been in the customer's favour (as has measuring of defects).