The value of rewards from cards like this have massively diminished in value in recent years. This started a few years back when there was a new regulation around interchange fees (which the merchant has to pay), so card providers simply couldn't afford to fund the rewards any more. (One of my clients is a big card provider, so I got very close to the the nitty gritty of all this at the time).
I have a JL card, and put EVERYTHING on it apart from fuel and supermarket shopping. The cashback used to equate to 0.5% (in JL vouchers), which was as good as you can get on any (unlimited) cashback card, but as someone said up-thread, they have recently cut this, so it's not that great now.
I also have a Santander 123 card and get 2% cashback on fuel and 3% on supermarket shopping (I think it's that way around), but it's capped and there is a fee for the card, so in reality I 'gain' about £3 a month. Not really worth it in the grand scheme of things, but we use it as a joint card for spending on food and fuel, so it helps our household accounting anyway.
If you shop at Tesco, that's probably going to be the best value card for you - the rewards are worth WAY less than they used to be, but if you shop there, it should still be worth your while.
On the Amazon one, you need to spend £4000 (outside of Amazon, so worst case scenario) to get a £10 voucher. Equivalent of 0.25% cashback.
If you are in the habit of putting all your spend on it, and paying off in full, then you may as well gain some form of cashback, but you're never going to get anything worth writing home about. Sadly, those days are over.
I know you said you're looking for a free card, but you might actually gain more from a fee-based card. If your habit of paying in full each month is well ingrained, and you know how you're going to use it, then you don't have anything to worry about re the fee - your bank may well offer one with cashback which offsets the fee. If you know how much you typically spend each month, you can see the level of cashback and work out whether you'd be better off.
The only other thing to consider is how you get your reward. Most cashback cards just take it off the balance, so you never see the money, and it probably only amounts to a few £ a month anyway.
The advantage of JL and Amazon is that you get a tangible voucher, so it feels much more like a bonus. I took advantage of the 25% off 6 bottles of wine offer in Waitrose when it last came out, and spent my JL vouchers that way - free wine definitely feels like a proper reward!