How portable do you need it to be? Older radios long out of production are usually the best bet for MW DXing. The Panasonic RF-2200 has long been considered the gold standard. They're regularly available on ebay though most sellers know the value of what they have and set prices accordingly. I have one and you have to get into very expensive tabletop communication receivers to do much better on MW.
Of current production radios the C. Crane CCRadio 3 (or 2E if you don't need Bluetooth) is one of the best. The new version of the CCRadio EP Pro, which you said you were considering, is also quite good. I have the earlier version of the EP Pro and it drifts like a dinghy in a hurricane. I ended up buying the CCRadio 2E to get past the drifting of the EP Pro. The newer EP Pro actually has digital tuning so it doesn't drift at all. The only issue is the analog dial making it more difficult to tell exactly what you're tuned to. You should probably check on the tuning step on the EP Pro since you're in the UK. I have no idea if it tunes 1kHz steps or 10kHz steps. Okay, just checked. It must have some way to switch between 9kHz and 10kHz steps. That's somewhat less than ideal but still workable. If you can afford the CCRadio 2E you might want to consider that as it can tune in 1kHz steps, allowing you to tune away a bit to avoid an interfering signal.
You might also want to consider a separate antenna. A tuned loop you can turn to null interfering signals can do absolute wonders for reception. There are a number of cheaper ones available. Crane has their Twin Coil Ferrite, which is good, but awkward to aim with any kind of precision given the cord coming out the end. Something like the Terk AM Advantage is going to be easier to maneuver. Or roll your own. There are guides to building one all over the internet.