There is bound to be some shortage simply because of lockdown. I think I read that there are c 700,000 drivers. If 5% leave each year (retire, move on, etc) you need 35,000 to keep up. During lockdown there was no hgv driver training and no tests for many months, I think testing took a long time to come back on stream. If it works out as a 12 month hiatus and the industry can't replace leavers then there is a shortage. During lockdowns full and partial net demand probably fell: lots of activities we didn't or couldn't do including filling our cars to get to work or go on trips, restocking high street fashion stores, etc etc. although home delivery boomed. Now demand is back 'plus some'. So part of the shortage must be covid related, the rest a mix of long term decline in numbers and the unmentionable B word.
I wonder, and its a genuine wonder, what effect rules on intra-country working have had. Under EU rules, any carrier (and airlines are a good example) could trade between any 2 points - a Norbert Detressangle truck could have come to the UK with French goods, drop them in (say) Leeds, take a UK load from Leeds to Dagenham, then a return load to France. But now we are no longer in the EU I don't think they can do that middle bit - UK to UK - and maybe that affects capacity.
I do have one partial answer. One driver - one truck so it makes sense to have the truck as full as possible. I'm sure schedulers are very good at that, it's the way to make the whole system affordable and profitable. But what does full mean? Capacity is limited by weight and volume.
You can't do anything about weight - a ton of bricks is a ton of bricks - but if you look around a supermarket you realise a lot of volume is just air. Stop shipping air. Sugar Puffs minus the puff. Corn, not cornflakes. Ban pasta that has a hole - spaghetti fine, penne is space inefficient. Suck the gas out of bags of crisps. Trebor mints, no Polos. As for the ambassadors Ferrero Rocher, pass them between heavy rollers and sell them as slabs. Marsh, without the mallow. Gouda good, emmental bad (space wasting holes). Nice cuboid choc ices, no wasteful delicate cornettos. I bet we can save 40% of the lorry trips to supermarkets, and there must be other ways to save space on a whole load of goods.