I would say posted in wrong section. It is a problem working out when a heater in a large tank is working as it takes some time. As an electrician I will use a clamp on ammeter and check current draw.
Of course you may be considering more than just if they are working. One should use a high ohm meter to check installation these use 500 v and a low ohm meter to test the element continuity these use at least 200 ma.
One of the problems is economy 7 is a tariff not a system and there are a few different ways to wire up. Some times there is a DNO controlled time clock other systems include a special meter which monitors the time the power is used and you have to set the clock yourself.
However I would repost in electrics UK section and give a lot more info. Pictures of electric meters would help.
I suppose it could be software controlled no reason why one should not have a PLC controlling contactors which could even have a SCADA interface but I think it has just been posted in wrong section.