What is wrong with our Potterton Profile 80E boiler?

It is about 20 years old but works very efficiently when ON. The trouble is the pump is on constantly (24/7) and the boiler keeps firing up even when the thermostat in the hall is off and the programmer is also set to OFF for both water and heating. Consequently the radiators are on all the time, all day AND ALL NIGHT. This is costly and wonder if it is a boiler malfunction or an electrical fault with the thermostat or timer or programmer. Plumber suggests to get an electrician in or have a new boiler! Any suggestions would be gratefully received.