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You do not need to self isolate as you arrived in the UK before 8th June, see here: https://www.gov.uk/government/publications/coronavirus-covid-19-how-to-self-isolate-when-you-travel-to-the-uk/coronavirus-covid-19-how-to-self-isolate-when-you-travel-to-the-uk
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Yes, you may show them the Government's advice.
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