A PCS Union spokesman said:
The issues of the last few days has brought to the public's attention what we have said for a long time, that ministers can't cut staff and expect to run the same service - not just on passport controls at Heathrow, but right across UKBA.
Clearly, the cuts already made have had a major impact and further cuts planned every year until 2015 will make the situation even worse.
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Mayor of London Sadiq Khan is backing the scheme.
A spokesperson said the lightning strikes had left the "aircraft fuelling system unavailable."
Nearly 1,000 properties have been left without power, and road users have been warned of potentially hazardous conditions.