Hi Heinz,
Adding to John's comments, another very common issue with these cars is the advance system of the distributor. Failure of the advance system vacuum pot causes much the same loss of power issues as you are seeing under acceleration.
There's a mechanical advance system as well that can get rusty and stick or the springs become weak or break. Generally if in good shape, that system could work up to a certain point, but sudden changes, like hard acceleration, or at higher RPM it would not and the engine would 'bog down' and sputter.
Your B should have the 45D4 Lucas distributor, which parts are still available for and a complete new replacement unit is still made and available from Moss or other catalogs.
Safety Fast!
Art