In fact, as this particular transmission line will be feeding into the UK national grid, its normal role will be backup for offshore wind.
That somebody else at the end of a different transmission line might want access to the battery would be a good reason to site it where those lines meet. Another might be that you need to minimize fluctuations on power going through your transmission line. But whatever the reasons, they certainly will not be trivial, and might be revelatory. Trivially dismissing the question adds no light.
Require vast investments to add the capacity to handle storage and would be less efficient.
Your proposal is basically to spend 20% to 30% more money, loses and extra 4-7% electricity every charge discharge cycle and gains effectively nothing which is why nobody is doing it.
> how you top up local storage during supply peaks when you haven't got a local surplus.
Peak + filling storage requires extra transmission capacity which costs money to build and energy to use.
> At the end of a different transmission line.
Transmission lines work in either direction and are generally set up as an interconnected mesh. You want redundancy from the solar power plant to customers, but you also want redundancy from batteries to customers.
