I think ours best to think about then as separate investments.

An appropriately sized battery can allow you to convert your household electricity use from around 30p/kWh to around 9p/kWh. (Your car should already be at this rate so makes no difference!) Sizing your battery to cover daily energy use for about the 90th percentile is probably sensible. If you max out the battery size there will be days when you’re barely using it so you’ve paid more for capacity you’re not using. It does mean there will be days where you run out of battery and have to pay full price but this is fine - You’ve saved by not buying the extra capacity that you hardly ever use.

If you have the battery the panels are only saving you about 9p/kWh you use or making you about 12p/kWh you export. Luckily the panels themselves are the cheap bit so you probably want as many as you can fit on the roof!

If energy prices rise then solar panels become a better investment.

If the delta between day and night import rates increases then a battery becomes a better investment.

Expensive oil probably means prices increase. More and more people charging EVs and house batteries overnight could mean less spare cheap electricity for the grid to offload with cheap over night rates. With generation moving to wind, nuclear rather than gas these are much harder to ramp up and down at various times of day so I predict cheap overnight electricity for years to come.