How much you need for an emergency rather depends on your obligations. Three to six months salary is the usual rule of thumb but that maybe too much if you spend not much.
On isas, if you have put £3,000 (or up to £4,000) in a shares isa, you can still put £3,000 in a cash isa.
If you have spare cash, certainly use youfr cash isa alowance first.
But the tax benefits of shares isas are a bit over-egged in my view, particularly if you invest for growth and not income. We get a capital gains tax allowance every year anyway, so you have to be making tons from your isa to see any tax advantage.
To my mind, overall, the most important factor is to save the money in the first place and it sounds like you are doing a good job

.