As Walrus said it would be best if we knew what type of SU carb you have. Perhaps they are even the Strombergs used on 60's vintage engines. In any event, if the carbs are HS6 (side float bowl) type SU's, then yank the choke control out all the way and visually check that the jet tubes have dropped. This can be seen as revealing a brass tube above the plastic jet assembly. If the jets don't drop with the control out, you must adjust the cables. SU's are terrible on a cold start without the jet drop (not a choke at all really). Both tubes should drop the same amount. When they do, the engine will fire up right away.
HIF and Strombergs use a fuel enrichment circuit, again not a choke in the usual sense, and rarely give trouble except to cause rich running when warm.