I'm sure it is very hungry, nothing's been done with it for years I think. We only just moved in and I've been clearing the garden etc.

What should I do to make it more healthy? Mix in multipurpose compost?

Best to check if these roots are attached to any major trees/ shrubs before removing them. Gently pull back the soil and see where they lead. Tamp75 has it right with well rotted horse manure. It should have been left out for at least 6 months to take away any harshness that may burn the roots of new plants. Spent mushroom compost or well rotted leaves can also be a great way to improve soil. Compost will add short term nutrients (nutrient content normally lasts around 6 weeks) but if anything tends to dry out soil. If there are trees casting shade and a rain shadow over the area then try pruning off some of the lower branches to let in more light and rain.