I've heard people lightly touch upon nerves King George V may have held in regards to revolutionary spirit following the Tsar and his family to Great Britain, but was that it? Were these concerns valid? Finally, following the death of the Imperial family, did George have any regrets about not granting them asylum? He must have reflected upon them in some way, was anything recorded?
Apologies if this is poorly worded, and thank you for reading!
King George V was involved in the questions over the imperial family's asylum, but he was only one player in the highly contentious politics of 1917.
The abdication of Nichols II in the wake of the February Revolution presented the Anglo-French governments with a conundrum. It was clear to both ambassadors on the ground and in messages relayed to London and Paris by the Provisional Government that the popular mood was quite hostile to the Tsar. However, the Western governments were on the horns of a dilemma. Their primary goal with regards to Russia in the wake of the February Revolution was to ensure that Russia remained in the war against the Germans. However bad it might appear to let Nicholas II and his family twist in the wind, Russia's continued belligerence remained central to Allied war policy. Prime Minister Lloyd George's telegram to the Provisional Government celebrated the February Revolution as welcome move by the Russian people to embrace the type of popular government "which the Allied peoples have been fighting for since August 1914."
King George V looked at Russian developments with a degree of alarm and initially supported a British-based asylum in March. By April though, the King's opinion on the matter had shifted. This was partly because of the King's own fears for the British monarchy in light of a wave of strikes and republican editorials, but also reflected the Romanov's own unpopularity within British elite circles. The King and his entourage worried that the monarch's image of being a constitutional monarch would be damaged by giving shelter to an autocrat, a situation that would be more embarrassing because of the government's celebration of Russia's newfound popular democracy.
The King's private secretary, Lord Stamfordham relayed George V's concerns on the asylum matter in April and the secretary increasingly badgered the government with reports of the Tsar's unpopularity within Russia and in the UK. Lloyd George's cabinet though did not need Stamfordham to cool them on asylum. The government would have been in the same position as George V if they accepted asylum where it would appear as if they were alternating between praising revolution and providing shelter to its enemy. Moreover, a number within the government blamed Nicholas II for the sorry state of Russian affairs in 1917 and was ill-disposed to rewarding a sovereign that had mismanaged his war. Nor was this sentiment just limited to the UK; the UK's ambassador to France Lord Bertie reported back to London that the French considered the Russian Empress Alexandra to "not only be a Boche by birth but by sentiment." Rumors of the Empress's dalliance with Rasputin, which had already become the fodder of (false) salacious gossip in Petrograd had already leaked out into the Anglo-French press. Ideally, the UK government hoped that a neutral would resolve this problem and Nicholas II would take up residence in either Sweden or Denmark, but these offers were not forthcoming. Nicholas II was a political liability for all concerned.
Whether or not George V should not reversed his initial support for asylum is a moot point because the chances of Nicholas II and his family leaving Russia were dim at the start of the February Revolution and only grew worse. The popular opinion inn the Petrograd soviets was decidedly against the Romanovs and the Romanovs and the weak Provisional Government did not want to provoke their ire. The Provisional Government's remanding the imperial family to Tsarskoe Selo under virtual house arrest was a means to placate the soviets while moving the family into the Russian interior. The Provisional Government's Foreign Minister Milyukov and his successor Mikhail Tereshchenko both wanted a foreign asylum but lacked the means to safely move the imperial family to an area where they could have been evacuated quickly. Moving the family to Murmansk was ruled out because it was feared the Petrograd soviet would block this move and take custody of Nicholas II on their own initiative. Since the Provisional Government had begun to renew a series of offensives against the Central Powers, the last thing they wanted was to make Russian domestic politics more combustible.
King George V's volte-face on the asylum matter contributed to, but did not create, the UK government's stonewalling on asylum. This proved to be important not because it denied Nicholas II entry into the country but because it provided a rationale for the Provisional Government not to aggressively pursue the matter. During the interwar period a number of Russian emigres such as Alexander Kerensky singled out the UK and specifically both Lloyd George and George V as being partially responsible for the eventual murder of the imperial family by at first promising and then denying asylum. While the UK government certainly did not want to provide the family asylum, such critiques are often beside the point in that there was no politically-convenient way for either the UK or the Provisional Government to get the imperial family out of Russia in 1917.
For his part, the King did not really express much remorse for his actions in the asylum affair. In June 1917 he had written to one of his former secretaries that he feared for Nicholas II's life, but there is no record of him pressuring the government to take action. Both in public and in private he railed against the imperial family's Bolshevik executioners, but never clarified his role in the affair. George V's personal friend the Conservative MP Henry Channon wrote in his diary in 1938 that the royal couple regarded it as a personal failure that they did not save the imperial family and that it "has ever been a millstone to both Queen Mary and King George." Yet such ex post facto guilt was reflective of the whole situation. While Nicholas II and his family were alive, they were an unsolvable political problem for all parties concerned. Even the Bolsheviks found that their solution to Nicholas II- a publicized show trial- was unfeasible and potentially damaging to the cause so they elected to cut the Gordian knot and execute the family. Only when the imperial family was dead did the concerned parties really treat asylum as a serious option and a road not taken.
Sources
Baxter, Christopher, M. L. Dockrill, and Keith Hamilton. Britain in Global Politics. Volume 1. Basingstroke: Routeledge, 2013.
Rose, Kenneth. King George V. London: Phoenix, 2000.
See the answer from /u/TheTeamCubed/ here: https://www.reddit.com/r/AskHistorians/comments/3j3b3z/how_did_the_british_royals_feel_when_the_russian/