Rodney I think there is larger political and national matters at stake in the British decision. Take WWI out of the equation and I believe they opt to make the rescue. But the Russians were still fighting the Germans. Not very effective mind you, but fighting non the less. If the Russians completly break off with the Germans, or worse switch sides this puts a lot of troops back on the Western Front to fight the Allies. Such a situtation could have very easily changed the entire outcome of WWI.
I'm not sure I get this. It's true the British and other Allies wanted Russia to remain in and be fully committed to the war against Germany. But even the Provisional Government was quick to assure its allies that they were continuing to fight. They underestimated anti-war sentiment and the soldiers' discontent, but at least at the governmental level there was real commitment.
And, IvanVII, the implication of your post seems to be that ,if Britain had offerred asylum to the Romanovs, then the Russian Provisional Government , because of that offer, would have bailed out of the war and made a separate peace with Germany. I think that's unrealistic. Whatever reasons the PG had to remain in the war were far more significant than a symbolic and wholly non-military decision such as a humanitarian gesture to a by-then civilian family , including five children and five females.
Rodney, I think you're looking at it from the point of view of the PG. I'm looking at it from the perspective of the British Goverment. I agree with you that it was unrealistic, but diplomacy sometimes foregoes realisim.