Despite this, the Bullock report (1975) which gave serious consideration to spelling reform and was split on it,
in 1953 the House of Commons had passed a Spelling Reform Bill which was predictably thrown out by the Lords
Oh Masha, why do you keep making stuff up? Or, as those less charitable might say, lying?
Bullock made no recommendations on spelling. At paragraph 6.21 he explicitly rules out considering it:
"Various solutions have been suggested to the problems presented by the irregular system of spelling in English, the most radical of which is its actual reform. We received evidence in favour of this measure, and it was suggested that we might include attention to it in our recommendations. The views of members of the Committee differ on the question of spelling reform, and this difference of opinion is probably a fair reflection of the range and intensity of the views held by teachers and the public at large. However, the majority of us remain unconvinced by the case for national reform of the system of spelling in English. We consider the issues involved too complex and the implications too far-reaching to enable us to stretch our brief to the extent of giving the subject the detailed study it needs. In the circumstances, therefore, we do not feel able to make a recommendation on it."
They were split on spelling reform in the same way they were split on whether to have thin or thick cut marmalade for breakfast: the views on a topic that was not part of the remit of the enquiry were different. They weren't "split" on it in any useful sense, and they explicitly gave no consideration to spelling reform.
But obviously, given you think differently, you'll have the evidence to hand to show us the "serious consideration" Bullock gave the topic?
Moving on, the Commons did not pass a bill on spelling reform in 1953 and it wasn't thrown out by the Lords.
The bill received a second reading and went off to committee, but was withdrawn shortly afterwards by its sponsors. In the debate, Labour MP James Ede said the bill would only confuse the less intelligent by making them learn two ways of spelling, a rather prescient comment. Presumably your studies of English preclude you spending as much time as might with Erskine May and Hansard, but the bill never went near the Lords, so they had no opportunity to see it voted down, and second readings are granted to pretty much all bills that are not obviously deranged. As happened to the first iteration of the bill you cite, which was voted down 87:84 in 1949 (and which reaches low farce when Isaac Pitman cites Cyril Burt in his favour: that's Burt the charlatan and fraudster, with his made-up researchers and false statistics).
When you're making stuff up, you might consider looking at your own organisation's website, which has the merit of, unlike you, being accurate: "The bill's sponsors realized that it was likely to meet strong opposition and it might be rejected by the House of Lords." Back in the real world, private members' bills which receive a second reading on a thin majority on tiny voting figures (65 to 53) have precisely zero chance of progression anyway, so blaming it on the nasty Lords is all a bit otiose. That this is trailed as the high water mark of spelling reform shows just how low the tide actually is.
In passing, the Bill in 1953 was only asking for a trial anyway. Had it passed, that trial would have been ITA, and it would have failed just as it did in reality. So even had the 1953 bill been enacted, the outcome (Pitman pushes ITA, it turns out to be a disaster, everyone goes home unsatisfied) would have been the same.
There's a nicely formatted version of Hansard for the debate here. It is a total car crash.