Ok seen this problem and it was due to a much higher volume / pressure being pumped by the fuel pump and flooding the carbs, find the correct pump or fit a fuel pressure regulator. Another problem is the needle valves may be also failing due to bad seating/sealing.
Prime suspect is to high a fuel pressure?
Morgans 1934 MX, 1947 Series 1, 1956 +4 TR4, 2000 +4 T16
Triumph Herald 1969 13/60
Morris 1970
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