More specifically, the current row can be traced to Tony Blair's anti-extremism taskforce, created less than a fortnight after the bombings, which invited Muslim leaders to advise the government how best to neutralise the "evil ideology" of extreme Islamism. The aim was understandable, but the execution was flawed. Many of those summoned to the government's table were individuals whom Blair had described as being part of the problem.
During cabinet meetings a month after the attacks, the prime minister fine-tuned the strategy for tackling radicalisation. Blair wanted to address extremism at its root causes. He wanted to build resilience in the Muslim community so ideas that spawned terrorism could be rejected by the community. In Gove's parlance, Blair wanted to "drain the swamp".
The thinking led to the creation of Prevent, the government's strategy to curb radicalisation which forms the centrepiece of the rumbling disagreement between Gove and May. It was revealed on Saturday that both have earned the ire of the prime minister with David Cameron ordering his education secretary to apologise over his comments and May's press aide, Fiona Cunningham, reportedly sacked as the political fallout continues.
Prevent hoped to disseminate a "counter-narrative" to that of fundamentalist Islamists, but quickly became dragged into the myriad turf wars between various Muslim factions.
In an early spat even the title of Prevent became a fiercely contested issue. On one side was Hazel Blears, chair of the party, championing the title "Prevent: Preventing Extremism", an expansive initiative aimed at the entire Muslim community.
Opposed were the then foreign secretary Jack Straw and chancellor Gordon Brown, who argued for "Preventing Violent Extremism", a strategy that targeted those engaged in, funding or actively supporting terrorism.
In 2007 the Office for Security and Counter Terrorism (OSCT) was created in the Home Office, headed by experienced civil servant Charles Farr, who quickly became Prevent's new poster-boy.
Fresh anti-extremism strategies emerged from the OSCT. Part of Farr's approach was to foster closer ties with non-violent Islamist groups to bring in violent extremists, an approach that critics liken to funding the BNP in an attempt to de-radicalise Combat 18.
Following the Conservative election victory in 2010, the current education secretary and cabinet allies such as George Osborne were unimpressed with Prevent's adoption of a more tolerant position, and particularly disapproving of the fact that controversial groups received government funding.
Gove wanted the "swamp drained" immediately. Yet his attempts were blocked by an alliance including chair of the party Baroness Warsi, attorney general Dominic Grieve and business secretary Vince Cable.
The clearest indication of where David Cameron wanted to take the government came three months later with a speech by the prime minister in Munich, which included a declaration that the coalition would not share a platform with extremist groups or fund their views. Cameron pledged to "turn the page" on the "failed policy" which saw Whitehall engage with and fund "peaceful" Islamist groups in the hope that they could coax individuals away from terrorism.
But Farr's OSCT has continued to award a number of extremist groups fresh public funding, including one charged with inducting new staff into the OSCT. Gove has become exasperated with this conciliatory approach.
Regardless of underlying nuances, Gove and May are simply the latest ministers to lock horns over an issue that has simmered since the morning 52 people were killed by suicide bombers almost nine years ago.
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