Economy 7 water not heating overnight

You should check to see if there's a separate fuse box for your E7 circuits (there should be). If there is, then there should be a fuse/circuit breaker for the E7 immersion heater. If there is, there's a possibility that it has blown/tripped, respectively. It's conceivable that an associated RCD (one that doesn't protect the radiators circuit) has tripped. If it's a circuit breaker and it's tripped, try switching it back on again and see if it works overnight or trips again. If it's a fuse that's blown, you'll need to get rewire the fuse with the correct rating fuse wire (probably 15A). Chances are - if the fuse/circuit breaker has blown/tripped - that it has done so for a reason: i.e. because there's a fault somewhere on the circuit. At which point you're going to need to get a registered electrician in to test the circuit. So why not take the easy route and get an electrician in at the outset?

Could be a loose connection, could be that the thermostat has failed (as this is often not replaced when a new element is fitted!), could be the overheat lockout trip on the thermostat (look for a small reset button). Could be that the circuit wiring has developed a fault. Similarly it could be a fuse that has blown? - In short there are numerous possibilities and really needs someone to take a look and run a few tests and checks.

There could be a thermal trip on the element. It would need the power turning off and remove cap form element top, if you look at the thermostat on top of element there may be a button that has tripped. Press it back in to check. turn power back on and check. If it continues it may be set incorrect or may be scale build up on element inside cylinder