The Arab Spring strengthened these anxieties. The Brotherhood did not initiate the uprisings but took advantage of the political turmoil. Mr. Morsi’s presidential triumph in Egypt made the Saudi regime fear that it might be challenged by newly emboldened Islamists at home. So Riyadh’s hard-line religious rulers supported a secular military coup against an Islamist president in Cairo and pledged $12 billion in aid. And in March, Saudi Arabia joined Egypt in declaring the Brotherhood a “terrorist organization.”

Western foreign policy, too, has been shaped by fear of instability and unrest. Britain and America are often the loudest voices proclaiming the virtues of democracy. In practice, they tend to take an instrumental view of its applicability. Autocrats who work in the West’s interests are generally preferred to democrats who challenge them.

Nowhere has this been more apparent than in the response to the Arab Spring. Where pro-democratic protests have challenged governments that Western powers oppose, as in Libya or Syria, the West has been keen to support those movements. But where they have risen against governments deemed useful to the West, the response has been equivocal.

For years, Western powers supported the dictatorial Mubarak regime in Egypt. In 2009, President Obama described Mr. Mubarak as “a stalwart ally,” while just days before Mr. Mubarak’s ouster in 2011, the former prime minister of Britain, Tony Blair, praised him as “a force for good.”

The West has been even more indulgent of the religious autocracies of Saudi Arabia and Bahrain. Both are important allies in the “war on terror”; both are major customers for arms exports, especially from Britain. There are close personal ties, too, between the British royal family and their Saudi and Bahraini counterparts. And Bahrain is strategically important for America, with the Fifth Fleet of the United States Navy based in Manama.

As a result, opposition movements in the two Persian Gulf states have been largely ignored by the West. When Saudi Arabia sent tanks to Bahrain to help in the bloody suppression of Arab Spring-inspired protests, Western allies stayed largely silent.

This is the background to Britain’s investigation of the Muslim Brotherhood. It is small surprise that it will be led by Sir John Jenkins, who happens to be Britain’s ambassador to Saudi Arabia. A key member of his team will be Sir John Sawers, the current chief of the Secret Intelligence Service (also known as MI6) — and a former ambassador to Egypt, from 2001 to 2003, when he acquired close contacts with Mr. Mubarak’s administration. The political character of the investigation could hardly be clearer.