Can a shower be placed next to the hot water tank (airing cupboard) or how easy is it to move the hot water tank?

Your shower should be positioned below the level of cold water storage tank. The position of your hot water cylinder is irrelevant - what matters is the difference in height between your shower head and the level of water in your tank in the loft. The cylinder could be level with it, above it, below it - it really doesn't matter. People, some plumbers included, seem to get confused between tanks and cylinders and this then causes confusion when calculating the head of the water required for a certain situation.

An instantaneous electric shower that does not need a hot water supply could easily be fitted next to the airing cupboard.

you can put shower next to airing cupboard if you want.If you wanted to move the cylinder you would be better to change it to a megaflow and place it in the loft(assuming you have space) this would do away with the need for pumps etc and increase the water pressure throughout the house.Cost for 210ltr megaflow plus fitting around £1,000.