Ignition is an easy check, but as mentioned if it starts and idles, then a fuel issue is more likely as the cause. New carb? Has it ever run as it should? If so, something has changed and anything restricting fuel flow to the inlet tract is suspect, from fuel, taps and filters, pipework, needle and float, main jet, emulsion tube drilling, throttle slide and needle. An air leak will also weaken the mix, so something else to consider.
The float and its needle work to provide a fixed level of fuel just below the top of the throttle needle jet, so fuel is to be expected under the main jet. Operating the Tickler holds the float down to raise this fuel level on a temporary basis, fuel then overflows into the bore of the carb to provide a slug of rich mixture to aid cold starting with a closed throttle. Float should have unrestricted movement to allow opening and closing of that float needle. Assembly error common on earlier monobloc carbs, washer in wrong place on tickler assembly.
A mechanical problem is unlikely, but I have had engines which would not speed up simply because the tappet clearance was too small, valves opening too early and closing too late.
Good luck with this conundrum, let's see if it is a simple fix.
Swarfy.
