Heathrow said 10% of flights with its biggest 20 carriers would be cancelled due to high winds.
“We do not know exactly how many passengers or flights that will have an impact on, although the cancellations are only expected for Tuesday,” a Heathrow spokesman said.
Gusts of more than 55mph are likely inland, but could reach 60 or 70mph in coastal areas.
Northern Scotland will have the highest winds – up to 80mph on the coast.
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The Met Office said: “The public should be aware of the potential for disruption to travel and possible damage to trees.
“Difficult driving conditions will result, perhaps exacerbated by surface water and spray in places.”
The strongest winds will coincide with the morning rush hour in places.
© REX/London News Pictures heathrow airport
Virgin Trains also warned that heavy rain might affect services on Tuesday.
A spokesman said anyone planning to travel should check before setting off. Customers with tickets for Tuesday would be able to travel on Wednesday if they preferred.
Hurricane Gonzalo – which at its peak sustained winds of 110mph – caused severe damage and a power blackout when it hit Bermuda at the end of last week.
Royal Navy ship HMS Argyll, with a crew of 180, has arrived at the British territory to help with the relief effort if needed.