[BAracer]

So...

I wired up the controller to a piece of track following the diagram supplied with the metal cartridge. I checked it three times.

STEP 1... What make of track?
A single piece of Scalextric Sport half straight

I switched the power supply on. 

STEP 2... Adjustable voltage power supply? Set to what Voltage?
It's the basis Pendle 13.8v fixed DC power supply

The green light on the controller came on.

And then things get a bit muddled...I am not sure which exact order the following things happened, but it was all within about a second.

I pulled the trigger

STEP 3... When you pulled the trigger all the way, did the LED glow Red? It should to signify reaching the end of the trigger throw.
I've seen that in the past when I was trying to get the 'Home' cartridge to work. Didn't notice it in that split second this time round. 

I put a Scalextric car on the track
The green light on the controller went out 

STEP 4... Digital or Analog car? As soon as you put the car on the track? Without pressing any button or pulling the trigger on the handle?
It is a basic analogue Bentley Continental. I switched the supply on. The green light came on. I just can't remember if the light went out when I placed the car on the track or when I pulled the trigger, I was in a hopeful frame of mind as opposed to analytical

I think I heard a sizzle noise

Now the green light on the controller doesn't come on, and the car hasn't moved.

If you start from STEP 1 again, the green LED does not light? If True then the fuse in the Cartridge probably blew, or something else has fried.
Yes, have tried it nine or ten time again, but no green light or car movement. I checked the 10A fuse and it looks intact. Could I try replacing it with a household fuse?

Shall I just bite the bullet and get another handle so I can check if my current one is just duff, or are there any simple tests I can do with the current handle to see if it is faulty?

There are simple tests but you should write down what steps you are taking and only do one thing at a time to confirm operation. Without knowing which track you've wired up, I would start with making sure the wiring to/from the PS and track are correct. It sounds like you have 2 wires swapped.

I followed this wiring diagram that came in the banana plug bag
   
I went by the colour of the bands on the three cartridge cables.

Thank you for your assistance DJP