Our old Valliant Turbomax is humming away with the central heating
light on, and every 5 mins or so firing up for a few secs and then
firing down, but both heating and hot water are turned off at the
controller.

I've noticed that the boiler pressure is over 2.5 bar.

It's an unvented system with a hot water tank and (blue) expansion vessel.

Am I right to suspect the expansion vessel - it either is failing or
needs recharging. I guess not a DIY job.