Kent Police say that although there is no intelligence to suggest any direct threat to anyone living in the county, it has deployed additional resources across the region to provide a presence in potentially vulnerable communities.
Assistant Chief Constable Gary Beautridge said: "We are working with local communities and partners whilst the Metropolitan Police investigate the full circumstances around this incident.
"We are providing high visibility policing in areas across Kent and would appeal for people to stay calm and work with us to ensure the safety of everyone in our county."
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Sunny this evening, then dry overnight. There is the risk of thundery showers for Kent tomorrow morning, then sunny spells by the afternoon
Sunshine to end the day then dry tonight. Tomorrow will be mostly dry and feeling fresher with the risk of a heavy shower in the afternoon
The video, obtained by ITV News, shows scores of migrants desperately trying to board lorries in a restricted area within the tunnel.