So the bike shop have agreed to send a replacement chain to the independent mechanic and have him revisit me to fit it.
They have said that a chain with the full 116 links was fitted but with no slip link and that this must be making the difference. But when the independent mechanic checked the chain he counted 114 links and said that it should be 116 and that's why it's too short and why some of the gears are unreachable.
The shop also advised me that I shouldn't be using extreme gears together in any case. Which as a cyclist who's been riding bikes with double and triple chain rings for many years I'm well aware of course. One might very rarely or never use extreme gears together but the idea that one would set up a bike in such a way that those gears are unreachable seems completely bizzaire to me. Why would you have a 20 speed bike but with only 18 that are usable!? Am I wrong?
OMG...
ok, a few points.
1) chains aren't all a standard length, you can buy shorter and longer ones and most bike shops will have a 50m reel of chain in the work shop for this reason.
2) you don't fit a chain and just hope it works, when you fit a chain you look at the length that is needed.
3) the chain on a full suspension bike often needs to be longer. Have a look at what happens when you compress the suspension, your chain stretches because the distance from the bb to the rear axle lengthens on pretty much all full suspension bikes. So if you can't get into 2 gears when stationary, when you're in the top one you can get into, it'll essentially lock out the suspension on your bike.
4) As you've said 20 speed bikes don't have 20 gears you should use, even if you can use them. But yes, no one should be setting up the bike so you can't use them, for a host of reasons, especially on a full suspension bike - see 3).
They are trying to wriggle out of what is SHOCKING incompetence, and have now resorted to a number of lies.