No. The pump should not run when the CH is off, it is an installation error or fault. No way is it some "modern way". It is also an utter waste of energy.

There is no need to have the CH or HW coming on "to keep it ticking over" when the house is unoccupied at times of no frost. Assuming you are not in a part of the world where it is currently winter and could suffer frost at the moment, just turn it off, anything else is a waste of energy. If it was a cool time of year (spring/autumn) I would say turn it back on half a day before your father returns, but in summer even that is hardly necessary. Even if going away in winter, you could turn the thermostat down to say 12 degrees for protection.

Even when your father is in the house. He only needs the HW to come on, say, twice a day for at most a couple of hours, in fact probably only once a day if he only uses substantial quantities of hot water once a day, like many single people. Absolutely no need to have the CH on overnight when he is asleep either, even in winter, assuming some kind of approximation to a modern standard of insulation. If the house is not insulated to an approximately modern standard, it is a no-brainer to have it done.

I read that the average energy bills for a house are about £900 a year. I live in a 4-bed detached house and my bills are half that, even though the house was originally built in 1938 with solid walls and has been difficult to fully insulate to modern standards, though we have done our best. Your father's situation makes me realise why so many people have ridiculously high energy bills.