The insurer said that there had been significant storm damage caused by high winds unlike in more northerly parts of the country where flooding was mainly to blame for the damage.
Forecasters predict that Saturday, 15th February, is expected to be the most hazardous day, with yellow warnings for wind and rain covering large swathes of the country.
Khan added: "Unfortunately with the rain that has already fallen, the additional significant rain that Storm Dennis could bring may cause severe flooding in some parts of the United Kingdom".
"At the moment we're looking at heavy rain on Saturday for all parts".
"Storm Dennis has the potential to bring very strong winds and transport disruption during Sunday and Monday morning", said a Met Office spokesman. Around the coasts, especially in the west and south, gusts of 60-70 miles per hour are likely.
Several fatalities were recorded during storm Ciara including a 77-year-old man from Clydebank who died after falling and banging his head during icy weather.
Met Office meteorologist Matthew Box said inland gusts could reach 50mph by Saturday afternoon.
Cross-border journeys between England and Scotland were severely restricted last weekend.
There will be speed restrictions on the rail network over the weekend.
An HCC spokesperson said the latest extreme conditions meant some household waste recycling centres may need to close at short notice this weekend, and apologised in advance for any inconvenience.
The combination of wind and intense rainfall can cause risky driving conditions.