Well, if your kitchen is cold, having an airlock over the back door will make a big difference. Plus, it's somewhere to ditch muddy boots, wash dogs, and close the door on all that crap.
Regarding the space, I wonder if so long and narrowness is the best option. An internal space 1.2 m x 2.4 m would be a slightly smaller area, but allow for two standard width appliances or kitchen units side by side at either end, without so much wastage in between. You could have your washing machine with a sink unit beside it, giving storage for laundry supplies. And at the other end, you could fit a massive chest freezer, or a 60 cm one with room for a tall mop/brush/cleaning supplies/overflow food cupboard.
Cons... Not sure, except for the expense of having it built. If you go for a pitched roof, it'll be more expensive to do, but a flat roof would be more expensive to maintain. And of course you'd lose a bit of garden, but I guess you're happy with that.
I'm so envious... I'd love a utility room, but the only we could do it would be to block side access to garden, and that would mean bikes and bins having to be taken through the house.