I do not know if British Milksheep and crosses thereof are available in the States -- they weren't ten years ago but I think they are now? -- and even if they aren't, there seem to be many more people breeding traditional sheep breeds such as Icelandics for milk production. So it is certainly possible to have "some reasonable amount" of milk AND a useful fleece. Particularly if you are willing to buy faraway animals and have them shipped.
However, that said, IMO if you want an efficient economical source of milk AND fleece, the smartest thing would probably be to buy one or two good dairy goats (note that in most places you can find someone willing to do driveway breedings to their buck so you would not need to own one, or do AI)
AND ALSO one or two sheeps of whatever breed has the wool you want. (You really need to research that, as there are vast differences in what different sheeps' fleeces are good for, between and even *within* breeds)
The goats would be a more time-and-labor-efficient way of getting milk, and for a larger time period before needing freshening (rebreeding); and the sheeps, which could be girls or wethers as you prefer or as convenient cheap sheep-supply dictates, need not ever be bred even if they are female, just use them as lawnmowers and goat companions and shear them once or twice a year
Mind you I say this as someone who GOT a coupla dairybred sheep for milking. I still think it's the right choice for me. But for you, maybe not so much (you definitely get more bang for your buck and more simplicity from separating milk needs and fleece needs and getting *both*. Or as someone said, just buying or swapping for a fleece)
JMHO, good luck, have fun,
Pat