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Technically, arriving at a port of entry without any visa is called seeking 'leave to enter' instead of 'entry clearance'. Entry clearance refers to a visa in your passport.
Those who do not require a visa for entry to the UK (non-visa nationals) may only do so if they are seeking to enter the UK for visiting purposes. For example, a US. citizen may arrive at a UK port of entry without any prior entry clearance so long as the main purpose for their trip is visiting. If they are seeking to work or study then they will be refused and told to apply for entry clearance beforehand.
Those entering from an EU country (also non-visa nationals) may arrive at a UK port of entry and will likely not be questioned about their purpose of visit, although they still may be. They are free to take up work or study while the UK is still subject to EU free movement.
In regards to the clean slate policy, if a citizen of a non-visa national country is refused leave to enter at a UK port, they are still free to attempt to enter the UK as a visitor in the future without ever applying for entry clearance however this approach is risky and is likely to offer the same outcome, therefore it is advised to apply for entry clearance. This way you will save yourself a trip if the application is refused. This is essentially the surest way to 'clean' your immigration history after any prior issues or refusals. Any subsequent applications for entry clearance will be assessed on their own merits however it is likely it will be refused if your circumstances have not changed since your initial refusal.
So in essence, a US citizen could travel to a UK port of entry as a visitor and for whatever reasons the Immigration Officer (IO) refuses entry and sends them back on a plane.
The US citizen can either attempt to travel to the UK again and seek leave to enter however this is risky and like stated earlier, will more often than not give the same outcome. US. citizen is best applying for entry clearance as a visitor and then using this to travel to the UK where, at the border, they will not be questioned and grilled as much and will be admitted.
That US. citizen can then travel to the UK on any subsequent trips without applying for entry clearance, although it will still be logged in the system about prior refusals. And of course, while it is acknowledged they were granted entry clearance, each attempt at entry will be assessed on how the traveller presents themselves to immigration on that day and the circumstances surrounding their purpose of travel on that particular occasion. But yes, applying for entry clearance after any troubles at the border or refusals is the best way to overcome any presumptions about immigrant intent and is essentially the strongest way to wipe the slate clean.