hi there richard, welcome to the forum!
ive had the same problem before, obviously the carb is flooding, so is the float itself not cracked? this is what i had on one occasion, rectified by a new one.
Secondly it could possibly be a worn needle valve, replace that too, which will be in the carb kit.
Thirdly it might be the fuel pump, but, try the other things first with the carb kit. (see below)
The carb kit is not much more that £15, and can be purchased from Ricambio International,
www.ricambio.co.uk where you will find there phone number.
my guess its the float or needle valve, have you put the float in a bowl of water to see if bubles come up / water gets in?
This spring you can see, might be off the needle valve itself, so if it is, then thats it solved replace!!!
i would offer to send you pics of the carb page in the workshop manual, but it doesnt go into detail on the inner workings of the carb.
Last thing richard, when you join the club you recieve a free BIS CD workshop manual, a 10% discount at ricambio and lots of other goodies, along with the prestigious fiat 126 club status :wink:
regards and happy 126ing
Chris