Hi, Smurfchops.
The Samsung A40 and A04s both use the same size SIM card. (it's actually a 'nano-SIM'). So you could simply take the card out of your old phone and put it into the new one. It would work straight way but you'd still be with Tesco Mobile (which uses O2's masts to provide you with a signal).
A better way of doing things for you might be to get a new SIM from, say, Asda Mobile. (I'm suggesting Asda Mobile as they use Vodafone's network, which might give you a better signal than you're getting O2. They're also one of the cheaper networks to go with and, as I use Asda Mobile myself, I'm happy to recommend their service).
With Asda Mobile you purchase 'bundles' to suit your needs. While it's possible to set them up as 'recurring', so that they're automatically paid for each month from your debit card (which is what most people do), there's no actual contract involved; you're free to swith to another bundle (or indeed to stop using Asda Mobile altogether) at any time. So you're not tied into anything.
If you only use your phone for calls and texts, plus (say) just checking the weather or the news from time to time (rather than, say, watching lots of YouTube videos) you only need to pay a fiver per month to get 3GB of data, plus unlimited calls and texts. A tenner a month will get you far more data though (12GB) which is more than enough for most people's needs. (That's the bundle plan which I use myself).
https://mobile.asda.com/bundles
Your new SIM will initially have a different phone number on it to your old one but it's a simple process to get your old number transferred over to your new phone:
https://mobile.asda.com/help/transferring-your-number/PAC-transfer
Once you've set up your email account on your new phone, you should automatically find that all of your old emails are on it. (i.e. you don't need to copy them across).
Everything else can be copied across by following the instructions here:
https://www.samsung.com/uk/support/mobile-devices/how-do-i-switch-my-android-device/