There's a disease called Blackhead. It can be carried by chickens without affecting them, but it kills turkeys. It doesn't exist in all areas of the world. In the U.S., some counties don't have it at all, and chickens and turkeys are safely kept together. In other counties turkeys cannot be kept with chickens, or on farms where chickens have been kept within many years. They county agricultural extension offices keep track of that sort of thing, and can advise people if Blackhead is a problem in their area. I don't know if this disease exists in the UK.
Heritage turkeys are excellent free rangers, and can fly quite well. Commercial turkeys, the broad breasted bronze and broad breasted whites, cannot fly well at all, and tend to be so large that they can only free range over a limited area. Given the size of an adult broad breasted commercial turkey, it could possibly intimidate a fox or badger, but definitely couldn't outrun it if the predator wasn't impressed by the size. A juvenile would be much more vulnerable. The heritage turkeys might suffer a few losses due to surprise attacks from an experienced predator, but could probably fly away from most situations given a few moments lead time, as long as their wings weren't clipped. A very large or older tom might have difficulty getting off the ground, but again their size might be intimidating. It all depends on the individual birds, and the layout of the land. If foxes and badgers are truly your only predators, then a well mowed field with some 6 foot high perches would likely be quite effective, as the predators would be easily seen and the high perches would be easily reached by the birds but not easily by the predators. A wooded or highly landscaped area might give the predators the advantage, as there would be lots of areas of cover for surprise attacks. The only differences in vulnerability between male and female would be size (males are between 1.3 to 2 times larger than the females, depending on your group) and egg laying or brooding. The females would be quite vulnerable on the nest.
Thankyou for the information. My landscape is very common english farmland, fields surrounded by hedges and trees dotted about, I also have a stream that is covered by trees and a small orchard. How would breeds such as bourbon reds and normal bronze turkeys cope?