I use Chip for automatic savings. It's an app - I have the android version. And you have to trust it, and give it access to one of your accounts - as in, type in your full details there, which gave me pause.
But otherwise, it looks at your balance, spending habits etc., and then takes money out regularly (prompting you each time, in advance, so you can cancel any individual transaction). You can set it to take out a "low", or "high" (which has never been above £25 for me, even though I just have a set amount sitting in the account, nothing moving, so if it were totally dumb, it would go "right, you're not using that, I'm going to yoink most of it") amount.
So long as it's not pushing you into trouble, it gradually builds up a balance.
I should have a referral link somewhere, but never mind that - https://getchip.uk