Hi All
Got my CT3 to the point where I was confident enough to test it on the road after having started and run it a dozen times in the garage.
imgur.com/sXGYJyU
I got a quarter of a mile before it spluttered and bucked then cut out. Subsequent kicking (the kick start!) would occasionally make it run for one or two seconds - so I pushed it home.
Stripped and cleaned carb again - no change.
Checked points (I hadn't looked closely at the ignition system before as it had always run so well) gap was a bit small but thanks to info gleaned from this site that wasn't necessarily a problem so continued to investigate. Bought a dial gauge, a flywheel puller and made a tool to hold the flywheel. Inspection showed the points and the condenser were new but I didn't trust the connection to the condenser - soldering was not good and insulation was burned back on the wires and it looked like the bare wires could touch or were touching the outside of the condenser. I got a new condenser, put a fibre washer on top and put shrink tubing over the top half of the condenser just leaving the contact exposed, then soldered slightly extended and newly insulated (shrink tube) wires.
Then checked and adjusted the timing.
After a couple of kicks she started - but only ran for a second - in other words still no good.
Next I decided to rule out the (new) spark plug (which was not sourced by me) so I swapped it with another new one which was in my CT1 project when I got it.
And that was the problem - now she runs perfectly - second test ride went without a hitch.
Yes I've had this new plug problem before with British bikes and I've read about it in this forum, plus when I change plugs I keep an old plug that I know works - but I still left it till last to check!!  

Good news in the end. 

Yes, a lot of crap repro/fake parts out there. 

Glad you got it sorted.  Looks like a lovely bike.

good instincts re trying another "new" plug! might have avoided a kick-inducted heart attack, or pulled hammy!

Good she's up & running now. My first thought was flywheel key let go but obviously not that. Enjoy your ride. Old saying-- stay on the bus route for a ride home but you're all sorted now so that's good.

Congrats  beautiful bike now you get to enjoy it 

Bike looks great! Congratulations!

Been there - did this. Glad you stuck with it and found the solution. I now stock and carry spare new plugs and put a cylinder head temp gauge on all fresh rebuilds. Kick Ride Learn

Nice Bike!
Have I mentioned how much I want a CT3?  They just never turn up in my price range.

Thanks for comments. Looking forward to getting it dirty!