Regular saver or easy access for small savings?

Hi!

I tried to post the other day and got sign posted instead, which was actually extremely helpful and I've been reading through the material. But when going through the info, I've become a bit lost.

I'm on an extremely low income, no debts etc and looking to start saving an emergency fund. It'll be small and irregular amounts, up to £200 but probably closer to £50 to £100. I can't find advice specific to starting savings like this. The default assumption is that someone is able to regularly save and has a normal income, or has some kind of assets already. None of that applies to me.

I can see that premium bonds don't seem to be worth it unless you have a decent amount in them, and I can see that regular savers have higher interest, but there may be months when I can't afford to put anything at all aside.

I have a flexible saver linked to my current account, but I mostly use this to put money aside when it comes in, then transfer it back when I need it. I think I would benefit from something more separate. It's also only got a 1% interest rate.

Is my best bet to find another flexible saver/instant access savings account with a better interest rate?