What is the problem with expansion - I would have just a short pipe run to
the
mixer tap ?

There's also the stored water to expand too.

Would I be best to arrange a longer run ? I've seen something about
vented taps - how do these things fit in with an ordinary mixer?

Vented taps won't help you. You need to get a storage type heater with
enough storage to do what you need. It will probably have a 3kW element or
thereabouts. You need to get the type with a built in expansion vessel. This
will contain the pressure increase as the water is heated without requiring
vented taps or long pipe runs.

Christian.