What's your budget?
I think phones these days start at 5" at least, more and more are 6"+. The aspect ratio of your S4 mini was 16:9.
Modern (!!) phones have an aspect ratio more around 19.5:9.
Aspect ratio is the relationship between the height and width of a display. It’s a measurement of how tall or wide a screen is.
It doesn’t tell you how big a screen is, just the proportional relationship between the height and the width, so on a 16:9 screen there will always be 16 pixels in one direction for every 9 pixels in the other.
Taking the Samsung Galaxy A20e as an example, to compare it against your S4 mini:
It is approximately 22mm longer, 9mm wider and a little thinner.
It weighs 34g more.
It has a 5.8" screen, not 4.3".
Aspect ratio is 19.5:9, against the S4 mini's 16:9.
Pixels Per Inch (PPI) is 296 against 256.
Processor is Octa core against the dual core of the S4 mini.
The cameras are better res: 13 and 5 on the rear camera (wide and ultra wide) and 8 on the rear.
The memory is bigger too and the battery is 3000mAh against 1900.
The A20e is £170 at CPW SIM free, or you can buy it cheaper PAYG with a £10 top-up.
It always pays to ask if it is cheaper to buy a phone SIM-free or PAYG at CPW, as most (but not all) of their phones are unlocked, even if you buy them PAYG with a particular SIM card.
If the phone is cheaper PAYG, what I usually do is put the SIM in an old phone and use the credit.
I also buy phones from Amazon. Worth a look there. Also, Argos have a good range of SIM-free phones too.
If it's not clear, do check before you buy if the phone is unlocked to all networks, then you are free to use any network you like: you are not tied to your existing one.