The engine technology looks remarkable, if not revolutionary. Is this a unique effort, or is this technology also being explored by other nations/corporations? If so, what sort of timelines are they on?
There is an entire Wikipedia article on the subject.
One could call the Apollo lunar module a SSTO vehicle, as it made it to lunar orbit with one stage. Probably not what you're after, but still.
Currently, there appears to be only one country other than Britain looking into the idea - the Romanians with their Haas 2C.
On June 1, 2012, Romanian organization ARCA announced that they are constructing an expendable rocket, named Haas 2C that will attempt to reach orbit in one stage. The rocket has 520 kg empty weight and can carry 15.5 tons of fuel. It will use kerosene as fuel and liquid oxygen as oxidizer. In Spring 2012 they have successfully tested a lightweight composite kerosene fuel tank. The liquid oxygen tank is being designed and it will also be made of composite materials. The launch is expected to take place in Spring 2013.
ARCA's site states that Haas 2C is an attempt at the Google lunar X-Prize. Their team page says that one of their goals is to create the Haas 2C to be capable of placing 300kg in LEO - quite impressive for a single stage rocket.