Hi John,
All good advice from Joseph, but from what you're describing, I'd say to take a look at the vacuum and mechanical advance systems on the distributor. A 69 B would be equipped with a Lucas 25D4 distributor, which is notorious for problems with the vacuum advance disc failing, often with the advance arm separating from the vacuum disk. This can happen on the later 45D4 type, but less frequently.
The mechanical advance can't handle any hard acceleration on its own and the engines seems to bog and backfire as it tries because the timing is not advancing, just as you are describing. I'd check the vacuum pot and the mechanical advance system (springs, weights, etc.) for damage, rust or wear
My old adage is 'if it feels like a fuel problem, it's probably an electrical problem' (and vice-versa).
This may not be the culprit, but it very much resembles gas starvation on acceleration.
Hope that helps you.
Safety Fast!,
Art