Having driven the car a small distance (up and down the driveway a few times) there were two apparent issues with the brakes. First and foremost, it was necessary to press the pedal a long way before they felt firm. Secondly, after bringing the car back into the garage, I did what I call "the blue towel test". The latter is a basic check for leaks where I take a section of new blue paper towel and gently apply to each joint or connection in the brake lines. After applying it, a leak in any particular connection will be apparent by a tell-tale dark blue patch appearing on the towel. I found tiny leaks on both the rear brake calliper connections - even though I couldn't see any dribble lines beneath the connections or any drips on the floor. On closer investigation I also found that a small puddle of brake fluid had accumulated in the recess on the back of the DeDion Ear as well. Being careful to get the correct imperial spanner on the job, more torque was applied to both connectors.
The next task was to re-bleed the brakes but after setting up the Sealey Brake Bleeding kit, I decided to pressurise the system to 20 psi and leave it for a couple of hours before re-trying the blue towel check. That was successful - no noticeable drop in pressure and no leaks detected.
This cycle of brake bleeding was made considerably easier by trying a different method of connecting to the bleed nipples. I decided to try a Brake Nipple Connector made by Laser Tools. This is a moulded silicon rubber connector that plugs straight over the nipple and can accommodate the different sized nipples on the front and rear brakes.
I did one round of the brake bleeding process - this removed a few small air bubbles from both the rear brakes, but the front callipers were clear. After this, the brakes felt satisfyingly firm and the pedal travel was much reduced - a surprising result given the small quantity of air removed, but every day's a sco day.