Black plugs indicates too rich - so worth verifying with the previous owner if new needles were fitted. To be sure, you can whip the dash posts off and undo the needle grub screw and read off the 3 letter needle code at the top (where the little spring clips on). Once you know, tell us.
Does it start from cold without much choke? If so, it sounds like the mixture just needs adjusting - so maybe worth srcewing both carb jets up 4 flats and see how you go. Asides from that, get the timing checked. But from you said, it's overfuelling.
The other thing that I thought of is you could have the dreaded waxstat carb jets which look like this:
rather than the earlier and superior red fixed jet:
Waxstats were fitted to the 1500 (and other BL cars) as a tweek to help with emissions. They have a small wax thermostat in the base which shuts off fuel as the engine warms up. The theory is that the petrol gets thinner with temperature so they throttle the fuel flow down a bit to compensate. As far as I recall, they just give trouble and when they fail, they fail very rich.
There is an easy fix. By prising the tin cap off the bottom, you can remove the waxstat and replace it with two penny coins
Just remember to put the little steel pin back. There are how-to guides around on the internerd if you need more guidance. Or you can see a guide here:
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