As you say there's a few current accounts that will give you decent rates on smaller amounts but you'll have to set up the minimum pay-ins as standing orders (which works on almost all of them, I've had a fair few). You can also do the whole switching-for-bonuses thing which is much easier than it used to be and will give you an OK return but is more work than most people are willing to put in.
However, if you're looking for something slightly better than what you've got now there are currently a fair few 1.5%ish easy access accounts available that you could just dump your savings in and make a fair bit more than you're currently getting. You can get 2-3% if you're willing to lock some up for a year+.
ISAs are irrelevant for most people since the personal savings allowance came in - if you're earning less than £500/£1000 per year in interest (depending on income) then you won't pay tax anyway.
moneysavingexpert.com has excellent round ups of this sort of thing.