All of these monarchy-in-exile scenarios are all well and good, but my sense is that had the Romanovs made it out alive, whether by German, British, or Grand Fenwickian hands, they'd become irrelevant in a short time as did the Hohenzollerns (they don't even register on the radar today).
I agree they'd be something of an embarassment wherever they wound up initially (betting on Great Britain or Sweden) and would quickly be shipped off elsewhere. Their best chance of long-term survival would be somewhere other than Europe altogether; perhaps South Africa or Argentina might work. These days, the Romanovs would be not much more than C list celebrities (a great-great-grandson of Nicholas might be notorious for gambling debts; a great-great-granddaughter might make the pages of Penthouse after visiting a nude beach, for example) and that's about it.