Craft that can take two or three passengers on dives of 300m are already being built and sold by firms such as Triton or Deep Flight, which is based in California and set up by UK marine engineer Graham Hawkes.
Its craft have appeared in James Bond films and have also been sold to Branson and venture capitalist Tom Perkins.
The depths achieved by these submarines are still relatively modest.
However, versions are now being designed to survive dives down to 1000m, depths normally frequented by military submarines.
"These should be ready for their first journeys in the next few months," added Lahey.
The prospect of craft able to take their owners down to the very deepest parts of the oceans will create the greatest stir among thrill-seeking billionaires.
These include the Challenger Deep, part of the Mariana Trench, near the Mariana Islands in the Pacific. There is no light here, 11,000m below the surface, and the water pressure is a thousand times that of the atmosphere at sea level.
Nevertheless, several companies say they are now designing craft that will withstand these colossal pressures.
"We will use a sphere of special glass that is more than four inches [10cm] thick for the main part of our submersible," said Lahey.
"It will give its three passengers an all-round view of everything that is going on down there - though, obviously, when we get very deep, we will have to use pretty powerful lamps to illuminate proceedings."
By contrast, Deep Flight Challenger, a one-person, high-performance experimental prototype submersible designed by Hawkes, looks more like a plane and uses hydrodynamic force to propel the craft down.
James Cameron's team has been building a craft that will cost around $8 million. He intends to dive to the bottom of the Kermadec-Tonga trench, north of New Zealand.
Deep down
11,000m
Depth which the prototype mini sub Deep Flight could reach.
8m
Length of the single-person craft, which has a Plexiglass canopy and carbon-fibre hull.
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