Sunak began his post by looking back at his childhood in Southampton and his early connection with cricket.
He recalled that his father's GP surgery was located between the Dell, Southampton's football ground, and Hampshire's County Ground. Going to games on weekends and during school holidays, he said, left him with a passion for sport and a belief in its importance to British life.
"When I was a boy, the Tebbit test was a matter of intense debate," Sunak wrote.
The former prime minister was referring to the debate associated with former Conservative Party chairman Norman Tebbit, who had questioned which cricket team Commonwealth immigrants supported.
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Sunak said the test, despite the criticism it received, was one that anyone could pass if they supported England because they saw it as home.
"Ten-year-old me passed the test without even knowing about it," he wrote, referring to his childhood in Southampton.
From cricket to the identity debate
Sunak said delivering the Marylebone Cricket Club's Cowdrey Lecture on Thursday had prompted him to think about cricket's place in British life and the country's current arguments over identity and integration.
He reflected on his own experience as prime minister, saying Britain had created a multi-faith, multi-ethnic democracy and that he had benefited from it.
He recalled being able to read a lesson at the King's coronation and light Diwali diyas at Downing Street with his daughters without controversy.
"But something else is going on - a risk that we start equating skin colour with nationality," Sunak wrote.
He said that after leaving office, a debate began over whether he was English because he was a "brown Hindu".
During the election campaign, he also recalled being shocked by footage of someone using a racial slur against him. He said the incident stood out because such abuse had not been a feature of his political life.
"But the Englishness argument was stranger still," he wrote.
"Call it the reverse Tebbit test. If you're not white, it no longer matters who you support at the cricket, because you can never be English."
Sunak separates immigration from race
Sunak also addressed immigration, saying he opposed illegal immigration and recalling his efforts while prime minister to deport people to Rwanda.
"I think the bar for legal migration should be high," he wrote.
At the same time, Sunak argued that wanting lower immigration and stronger integration did not require accepting the idea that British identity should be determined by race.
"It is entirely possible to want a radical reduction in immigration and a far more robust approach to integration, and still totally reject the attempt to turn Britishness into a DNA test," he wrote.
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He returned to the question of how people born and raised in England should be viewed, arguing that their connection to the country should not be dismissed because they are not white.
Cricket as common ground
Sunak also pointed to cricket as a way of bringing different communities together.
The sport, he said, is played by nearly every major ethnic group in Britain. He compared his largely white rural constituents in the Dales with British-Asian children in Bradford and said cricket was something they shared.
"If cricket can produce England teams in which every kid can see themselves, the impact will reach far beyond the boundary," Sunak wrote.
He ended by returning to the sporting theme with which his post began.
"We must all be on the same side, cheering for the same team," he wrote.
"We cannot allow race to be reintroduced into our politics. We cannot allow Briton to be set against Briton."