This has happened a couple of times with friends' bikes now: the front changer is aligned ok, chain not rubbing against the changer in low or high gear, but it's slow and noisy to change up from 1st to 2nd, and from 2nd to 3rd. Have played with the tension adjuster on the gear lever, but this doesn't fix it. Does this mean a new gear cable is needed?

sounds like the cable is stretched. Tighten it with the adjuster on the mech itself, not the shifter. If need be, loosen the clamp and pull a bit more cable through.

Take it to a proper (specialist not Halfords and the like) cycle shop and get it fixed

It sounds like the cable has stretched thats all and need adjusting.
If it is a new bike then that will be it.
You could try adjusting the rear derailler this may solve the problem to.