First, 30 to 40 ebook readers still in their boxes is going to take quite some space, and weigh a decent amount.
So the first issue is that it’s likely to exceed your carry-on allowance, either in size or weight. You mention a separate bag/box for them, but most airlines won’t allow you to have multiple pieces of carry-on. This all depends on the airline, class of travel and fare, so it’s difficult to say more (we don’t know either the size or weight they represent).
It’s more than likely you’ll have to put those in checked luggage. If you manage to fit within the allowances for hand luggage, yes, you’ll have to put them all in separate trays at security if they require it for electronics (not the case everywhere depending on the equipment they have).
The second issue is related to the batteries in the devices. For safety reasons, there are regulations on the number of Lithium-ion batteries you can carry, which are summarised here. In your case, it’s likely you’ll have to abide with a limit of 15 devices with a battery.
As alluded to, there will be issues with customs. If this is a temporary import, your best bet is probably an ATA Carnet. Otherwise (if the devices stay in the destination country) be warned that in some countries, customs for passengers at the airports (the “red lane”) are NOT able to process commercial imports (which this will be deemed to be). If that is the case (no idea for the UK), the items will need to be handed over to an agent which will process them for you, which takes time (days, not hours) and costs money (in addition to taxes).
So it’s not an easy proposition, but with the right preparation it’s possible. I’ve been on projects where we had hundreds of tablets for an event which were carried by air (as checked luggage, in special protective cases), temporarily imported (with an ATA Carnet), and exported and flown back.
A (somewhat) easier alternative is to ship them (via UPS, FedEx, DHL, etc.). It’s often cheaper than the extra baggage fees (especially if you can wait 3 days), it’s often more convenient (they pick it up and deliver it directly where you want, you don’t have to carry them yourself). Pay attention to regulations regarding batteries (which are different from those for passengers) and customs issues (temporary imports are probably a lot more difficult).