Britain and Spain in 1917 did not compare.
Britain was involved in a world war which cost it 1700 casualties per day. A war that was ruinous for its finances and which might have been lost. The government had had to contend with an uprising in Ireland in the previous year and in 1917 had seen parts of the French Army mutiny and revolution in Russia.
Why should it have involved itself with the internal politics of Russia -whose government was committed to continuing the war?
OK. How woud have the offer of asylum to the Imperial family affected the war effort? Would have the trade unions started a strike at the munitions industry? Maybe the coal miners? A general mutiny in the army? Or would a revolutionary mob have stormed Westminster Palace and the House of Parliament?
The answer is: in no way. There would have been some angry articles in the radical press, maybe some small meetings or demonstrations and everything would have been forgotten in two weeks, once the Imperial Family settled for a quiet family life away from public attention.
Britain was involved in a world war, Spain was a neutral country. True. But the risk of revolution was much higher in Spain than in Britain. Alfonso XIII, the Spanish king, had survived three assesination attempts by 1917 (when he was 30). Canalejas, the Prime Minister, had been murdered by an anarchist in 1912. Dato, another prime minister, would be murdered in 1921 (How many PM were murdered in Britain during the XX century?). There had been a mutiny in Barcelona in 1909 which left more than 100 casualties. There was a revolutionary general strike in Spain in August 1917, organised by the Socialist Party. Anarchist violence and murders were almost a daily occurence...
Whereas in Britain all was quiet on the labour front. There was a special intelligence service headed by Basil Thompson of the Special Branch of Scotland Yard, who made weekly reports to the Cabinet on the labour situation throughout the country. Lloyd George, the British Prime Minister, was no friend of Nicholas II. He could have vetoed the asylum of the Imperial Family if he thought that their coming to Britain supposed a risk for the safety of the country. He didn't. It was the King (a constitutional King, as some here have remarked) who overruled the decision of his Prime Minister. The Easter Rising had nothing to do with revolutionary socialism, as neither the mutiny in France had (which had not yet happenned, so it could not have influence George V's decision). Nor did George V or his secretary, Lord Stramfordham, claim that there was an imminent risk if the Imperial Family were admitted to the UK: "all sort of difficulties", "it will be akward for Our Royal Family", "compromise the position of the King and the Queen", "serious embarassment".
George V was not thinking in terms of revolution and mutiny. As Kenneth Rose, George V's biographer, wrote: "The King feared for his popularity". And that's the reason he abandoned the Russian Imperial Family to their fate.