Cameron, who is concluding a three-day tour of India, said he would change the UK visa system to allow Indian business people to get a visa in a single day.
The BVEP is calling for him to extend the move to create special visas for overseas attendees for events with more than 2,000 visitors, saying it would make the UK events market more competitive.
A special event visa would be similar to visas issued to those involved in the Olympics in 2012 London Games, highlighting the purpose of the visit and allowing attendees to be processed in a streamlined way with special facilities for the events they are attending.
Michael Hirst, chair of the BVEP, said: "The Olympics and Paralympics have shown how beneficial it is to issue special visas to dedicated groups. Britain has also issued special visas in the past at short notice to attendees of football championships as well. Extending this practice to all large-scale events would help the issue process and create opportunities for a special welcome at entry points."
Hirst added the move would be a "real legacy benefit from the Olympics" helping the government to secure the £2.5 billion that was estimated to emanate from the visitor economy after the games.
Special event visas were a key recommendation in the It has previously said that Britain's events are at a "clear disadvantage" compared to other cities around the world whose events benefit from more government support and reduced rates for attendees.
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