According to Official Guinness Records,
The fastest time to run one mile carrying a 40 lb pack is 5 minutes and 16.9 seconds, achieved by Lee Riley (UK) at Cumberland Sports Ground in Crewe, Cheshire, UK on 12 November 2011.
Lee ran 1609.344 m carrying a weight of 18.1 kg.
For a complete list of 2011 records, please visit 2011 Guinness Records in United Kingdom.