Modern Vespa

My 03 Gt125 cuts out at lights etc when cold, battery charged, new plug, new choke, cleaned carb out, what else could it be?

Your idle adjustment could be a little low and might need to be increased. Drive the bike about for 5-10 mins to get it warmed up properly and then follow the procedure here:
GT 200: Adjusting the Idle
It's for the GT200 but the 125 is the exact same. I did it with a tacho, but if you don't have one, just increase the revs until the back wheel just starts to spin, then back off a quarter turn, You will get the feel for it.

FYI, here is the maual for the GT125
http://www.wotmeworry.org.uk/manuals/Vespa/GT125%20GT200%20Euro2/GT125%20GT200%20Workshop%20Manual.pdf

When were the valve clearances last checked (intake in particular)? If not for several years (or maybe never) then that's something to eliminate. It's the number one cause of Leader engines becoming difficult to start, or having poor running or stalling issues when cold. With a bike in regular use, the idle settings shouldn't need adjusting, and although doing so may appear to alleviate the problem it'll only be masking it.

HI Jim,
Just looking on the wiki about this procedure, may attempt it at Xmas, but the specs on the wiki are for the GT200:
The GT200 valve lash specifications are:
intake 0.004in (0.10mm)
exhaust 0.006in (0.15mm)

Do you know what they are for the GT125? I looked in the manual but no luck yet.

thanks all, I'll have to take it into shop as only worked on geared vespas before, wouldn't know where to start with valve clearances can do idle, got the manual cheers

They are the same.

Thanks Jim !! Great help as usual.
I might try this over the Christmas period, I'll study the wiki but it might be beyond me...