In their letters, the associations draw attention to the detrimental impact that the closure of Earls Court will have, not only on the exhibitions and events industry, but also on the wider community.
The associations want Cable to support their demand that the planning applications relating to the Earls Court Opportunity Area be called in, so that the government can judge all the evidence through a public inquiry.
Earls Court brings 2.5 million visitors and 300,000 exhibitors to West London every year, generating more than £1 billion in revenue.
The associations say that despite the UK exhibitions and events industry generating an annual expenditure of £11 billion, the sector is constrained by a lack of sustainable exhibition space.
Paul Woodward, managing director of UFI, said: "Demolishing Earls Court could set a potential UK growth industry further behind key international competitors. There is no evidence that London needs less exhibition space. In fact, the UK competitors are currently expanding their own capacity precisely because they understand the economic benefits the centres and the events that they host create."
Karim Halwagi, chief executive of the AEO, said the potential loss of Earls Court would be "enormous", not only for the UK exhibitions and events industry, but also on attracting foreign companies to exhibit and stage their own events in London.
"The irony is that UK Trade & Industry deeply wish to attract foreign event organisers to the UK but we already have a shortage of venue stock," he said.
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