To me it looks like after making the fuel pipework safe and fitting the filter (using proper fuel line clips,not jubilee clips) you need to sort out connecting the distributor vacuum unit to the pipe on brass pipe on the carburettor then you will need to carry out checks on the fuel and ignition system.I would start with ignition,check/replace and condensor points,set the points gap,verify with dwell meter,check the timing and vacuum advance,then set the carburettor up properly.First get the engine warm and then switch it off checking that the choke is fully off,top flap right open and the stepped cam fully off.Then set the idle stop screw.Screw it right out then back in so it just touches the cam then another 1/4 turn.Then set the idle air screw so it only just idles.Then set the mixture screw so that you can get it idling at the highest speed.Then screw it in until the engine speed drops a bit then set the idle air screw properly.If you have problems after that you need to investigate further.
But before all that,sack your previous mechanic if he can't do all that himself.Should be able to do all that in under an hour and parts less than £20.