There is no record of Iceland's visa refusal in the UK.

There are information sharing agreements between Schengen countries, but Britain is not a Schengen country and does not belong to the European Union. There are some information sharing agreements between Britain and Schengen countries, but these agreements usually involve security and counter-terrorism, and do not involve personal visa records. Therefore, the Icelandic visa was refused, and the British border inspection may not directly find this record.