Though Nutford House is a 40 minute walk (or 33 and a bit if you put some thought into it), most of that is walking through Hyde Park and you'll get to see dogs go mental all the time. And is 40 minutes such a trek anyway? From my experience of Nutford House, I'd certainly recommend it to Heythrop students. As well as being close to Hyde Park, you've also got Regent's Park just up the road and Edgware Road literally road the corner, which is certainly an experience. Oxford Street is barely minutes away, but the real gems are the little side streets off it (such as Marylebone High Street or St. Christophers Place). The whole Bloomsbury area (UCL, Senate House, British Museum etc.) are about 30 minutes walk away too, so the central location is definitely worth considering.
The only drawback I've experienced is the isolation from Heythrop students who live in Alban Halls and the feeling of being in lectures with complete strangers all year and only recognising people on my course, but that's just me and there's two more years to get to know people.