I currently have 14 solar panels on the house
If you were installing a new system I'd be saying "put up all the panels you can" - pay for scaffolding, inverters, initialisation etc. once and the incremental cost of more PV panels would be a small amount, pro rata. But you may have already covered your available roof area ...
If I understand my research so far, batteries will charge from the panels during the day and then in the evening I can use Octopus tariff to top up the battery and charge the car?
Yes. Best part of nothing from PV in Winter (10x more mid Summer than mid Winter)
Not a huge amount but easily enough to keep going with some sensible appliance management.
No disrespect intended, but that's a Boy's Own solution
I have "gear" scattered all over the house. My PowerWalls will power the whole shebang, but in a prolonged powercut I do go round turning off everything that I can to eek out the battery ... but finding it all is a bit of a challenge and a PITA. AM I guessing right that with Givernery it would trip if you didn't (first) turn off all non-essential appliances to get under the "limit"?
I wish (as in "I wish I wish I wish I wish ...") that when I recently had the house rewired the Sparky had say "Do you want to separate essential circuits" and then I could have just thrown a breaker to OFF everything unnecessary ...
My own view with which others may disagree is design the battery storage system for the particular needs of your house and power tariffs rather than around the needs of charging your car.
I agree.
My objective is:
In Winter: Battery sized to go from end of Off Peak to start of next Off peak (or majority of) - so that it is charged from Off peak and using scraps of PV if there is any
In summer: Battery size that will go from Sundown to Sunup - battery then charged from Sun each day and import nothing from the grid for days on end until a cloudy/rainy day happens, and any excess put into the cars. (I have 48 panels and in Summer that powers the whole house, charges the PowerWalls and I also get about 1,000 miles a month into the EVs)
Of those two the second is probably more achievable
I don't know the details, but the Tesla Power offer might be worth a look if you have everything-Tesla. They take control of your PowerWalls, discharge to Grid when they can make money (e.g. as a Peaker Plant) and charge/pay you same for Grid Import / Export - flat rate day and night I think - for someone for whom their formula works I expect its a very competitive rate?
Other than that, as others have said, PowerWall will run the whole house in a power cut (and for most powercuts the Gateway will switch without any break in supply - you'd only know you had a powercut if you checked the "Outage" list in the APP)
But I expect the wait-time for PowerWall is circa 12 months, and Givenergy seems to be shorter
Make sure that the battery can charge 0%-100% within the length of Off Peak that you choose.
P.S. I don't think the EV you have (e.g. Model-X) is relevant - you'd charge that on Off Peak, or from excess PV, whatever model it was. Having a Tesla might make it a bit easier to integrate Car Tesla Car and PowerWalls, but I would choose on other criteria.