Craven and rotten - well far less craven and rotten than that long long long list of countries who refused to give european jews entry visas as Germany increased its anti jewish legislation through the 1930s.
You do have to see it from George V's point of view - and his overriding responsibility was to do what Nicholas II couldn't do or failed to do which was to ensure his country's survival and the survival of the monarchy. That isn't craven or particularly rotten by the standards of the time. The war had dragged on, hundreds of thousands were dying and the British establishment was facing a growing left. With hindsight George V and the British throne seem completely unaisailable but that is with the benefit of hindsight and isn't an accurate picture of the situation. George V's biggest advantage and the key to his survival was his willingness to continue being what he became most admired for - a rather dull and dutiful man.
The interesting part of this is that no matter how many times you read the documents from the British Foreign office and compare them with activities in Russia at the time to show how narrow the window was for Nicholas' escape and the failure of it can't be laid at the British Government or King's feet.
Here's a selection of the UK foreign office files, reports and telegrams relating to the abdication and offer of Asylum
16 March 1917 Report that Empress and her children in Alexander Palace under guard.
16 March 1917 Report suggesting whereabouts of Tsar unknown
18 March 1917 Report suggesting future of Tsar
19 March 1917 Telegram to the Tsar from the King expressing distress at the turn of events, and professing continued friendship
20 March 1917 Miliukhov's enquiry as to the possibility of the Tsar going to England.
21 March 1917 Report of conversation with Dowager Empress about the Tsar's plans, and telegram stating that Tsar given permission to go to Tsarskoe Selo and then to Port Romanoff
21 March 1917 Report of possible arrest of Tsar
21 March 1917 Report that Tsar deprived of his liberty and placed under escort
21 March 1917 Telegram concerning the advisability of the removal of the Tsar from Russia, and the feasibility of him travelling to England
21 March 1917 Telegram conveying the King's offer of asylum to the Tsar
22 March 1917 Minutes of War Cabinet decision to issue invitation to Tsar to come to England for the duration of the war.
23 March 1917 Telegram concerning the provisional invitation to the Tsar to come to England
24 March 1917 Note that Tsar at Headquarters Staff
24 March 1917 Assurances received as regards safety of Tsar
24 March 1917 Telegram concerning request to Russian government to give Tsar safe conduct to Port Romanoff for departure to England.
25 March 1917 Assurance from Russian Minister for Foreign Affairs regarding the Tsar's safety
26 March 1917 Report that King's telegram not delivered to Tsar through fear of misinterpretation
28 March 1917 Thanks conveyed from Russian Minister of Foreign Affairs at being asked to cancel King's telegram
30 March 1917 Letter expressing the King's personal friendship for the Tsar, but doubting the advisability of the Imperial Family coming to England
2 April 1917 History of proposal that Tsar come to England
9 April 1917 Report of conversation with Kerensky concerning delay of Tsar's departure from Russia pending examination of seized documents
13 April 1917 Report that public opinion against Tsar coming to England, and against the King for supporting him. Suggests Tsar go elsewhere
15 April 1917 Telegram expressing agreement with view that Tsar should not come to England if any danger of anti-monarchist movement
17 April 1917 Letter stating that the King, while devoted to the Tsar, was now held to be anxious that the invitation not be taken up, due to public opinion
22 April 1917 Letter expressing relief that British invitation dropped, and opinion that the Imperial Family would not be welcome in France because of the Tsarina's German birth and leanings
23 April 1917 Suggestion that Tsar could go to France for duration of the war
28 April 1917 Parliamentary Question concerning the future domicile of the Tsar
The formal offer was made on the 2rd of march as late as 9th April Kerensky was being asked about delays to the Tsar's departure. Those early critical delays weren't coming from the British end - British doubts only surfaced in mid April culminating in the offer being withdrawn. In fact by the time Britain withdrew the offer the Soviet had already demanded and received assurances.
According to the French Ambassador - Miliukov thought the offer on the 23rd March only a week or so after the abdication was too late for the deposed sovereigns due to the growing anarchy and the power of the Soviet.
In his memoirs the ambassador notes this for March 24th - Saturday, March 24, 1917.
"The Soviet has heard that the King of England is offering the Emperor and Empress the hospitality of British territory. At the bidding of the "Maximalists" the Provisional Government has had to pledge its word to keep the fallen sovereigns in Russia. The Soviet has gone further and appointed a commissary to "supervise the detention of the imperial family."
Sunday March 25th:
"The Provisional Government have informed the Soviet that, with the approval of Buchanan, they have not given the Emperor the telegram in which King George offers the imperial family the hospitality of British territory.
But the executive committee of the Soviet still has its doubts and has posted "revolutionary" guards at Tsarskoïe-Selo and on the roads leading from it, to prevent any surreptitious abduction of the sovereigns."
In effect there was less than a month for Lvov, Kerensky and Miliukov to have the imperial family moved and they didn't do it. Not because of anything their allies did but rather their own inability to risk the widespread condemnation amongst the soviet that the move would have caused. It is clear from other stuff that the French (where there were huge celebrations by the socialist left over the Russian Revolution) weren't keen on offering asylum (despite a more sympathetic ambassador than Britain) and the neutrals didn't offer till 1918.