For those of you not familiar with the London Transport system, you may have resorted to getting to Kensington Olympia by Taxi or Bus, as there does not seem to be a way of getting there by rail (unless you opt for the morning service from Clapham Junction - in itself a possibility for some extremely rare Class 09 haulage!)
The nearest tube station is High Street, Kensington. This is almost a mile away along Kensington High Street.
To get to Kensington Olympia at any time of the day (when the Clapham Shuttle, or "Kenny Belle" is not a realistic option) simply take the tube to High Street, Kensington from any London Terminus, and walk from there.
For more details surrounding the curious Clapham Junction - Kensington Olympia service at the time, I suggest reading A Beeching Epilogue: The Curious Case of the Clapham Junction Ghost Train
Now there is no excuse (apart from the amount of points required) not to bag those Cricklewood Class 25s!