The Border Leicester ( or similar) has already been used to produce the mules, which are a maternal strain - ie big milky sheep bred to produce good lambs.
BUT in order to produce "good lambs" you need to cross the ewes with a terminal sire, ie one that will produce very meaty lambs. So you don't want anything with Border Leicester in. You want to use, for example, Texel, Suffolk, Blue du Maine, Charrolais etc not just any cross breed mix. You'll find plenty in the stores market - good enough to breed from, just not extra good enough to register. Or look on such as Preloved, where you would most likely be able to see the parents.