That's the issue with dedicated mud tyres, their benefit in mud is less than their drawbacks on hardpack. Even the best medium mud tyre (like newest Spec Hillbilly or Maxxis Shorty) aren't that much better than Assegai Maxxgrip (only available in 2.4, 2.6 Assegai is absolutely different tyre, worse one and only in Maxxterra and special worse Maxxterra but they don't even mention that on website) or Magic Mary Ultrasoft 2.4 (again, not to be compared to absolutely any other type of Mary, difference in Soft vs Ultrasoft is massive).
But if I lived in UK, I would probably use the newest Specialized Hillbilly, it's the best mud tyre that doesn't suck elsewhere. It can be used as universal tyre for almost everything but dusty hardpack.
For deep mud, only true mud tyre like Dirty Dan or Hydrotal work, but those tyres are pretty much unusable elsewhere, it's why even downhill racers hesitate to run them unless it's total full on raining during the race. I would take that as a hint and avoid them. When those tyres shine, it's probably best to just stay home.