jeff coming online at midnight in the depths of winter takes me close to my 100A fuse limit
If you want to reduce the impact of the Givenergy battery charge on your import, leave the timed charge window to the same as your E7 tariff, set the Charge to 100% and reduce the charge power to say 900W, or whatever you want, to get the right amount of charge in the battery by the end of the charge window. You could delay the start by an hour or so, but if you have the same window as the storage heaters, the inverter will prevent discharge to the storage heaters for the whole period. Of course, you will probably want to increase the charge power to soak up the PV during the day, but if you didn't, it would just divert to the immersion, so wouldn't be lost.
We used to have storage heaters and did blow our DNO fuse at one point, after many years use, and they replaced it with a 100A fuse. They are BS1361 and so can carry 1.25 x Full Load Current for up to 4 hours, although I'm not suggesting that you overload the consumer unit at all. There are two things that you could do to secure your supply better. One would be to get a sparkie to install an 80A fused isolator after the meter and before anything else. That way, if you exceeded 80A for any length of time, your 80A fuse would blow and you could replace it at your convenience rather than having to call out the DNO. Another thing you could do is ask your friendly sparkie to put some of your storage heaters on a separate consumer unit and energise that with a contactor on a time switch so that it comes on a couple of hours after the first set. The idea here would be to allow half the storage heaters to start charging at midnight and then start the others charging at say 2am when the first batch had had at least some charge. Obviously with this scenario, you'd probably want to put the larger heaters to come on at midnight and start the smaller ones later in the night. Also, EV chargers (at least our Zappi) can be configured to limit the charge to the EV so that the total import from grid is kept below a threshold that you can set. This means that if you are pulling 70A and you've set the threshold to say 80A, the EV will charge at 10A until heaters get to temperature and switch off, at that point the EV charger should ramp up its output to keep the grid import at 80A (or below).
It's the ability to flex these parameters (when you're asleep at night hopefully) according to a set of rules which suit your lifestyle that leads to home automation, ultimately, for most of us.