I'm going to focus my answer on the main wave of Cold War era British decolonisation in Africa, parts of Asia, the Caribbean and South Pacific in the 1950s, 60s and 70s. What these countries have in common, in terms of their constitutional history, is the process of independence was contingent upon constitution-making; in almost all cases a constitution was agreed - with the consent of the British authorities - before independence was granted.

So this answer will exclude the 'Old Dominions' (Australia, New Zealand, Canada, South Africa), whose path to independence started earlier and unfolded more gradually. It also excludes the three large Indian subcontinent countries (India, Pakistan, Burma) which achieved independence in the 1940s, since these countries did not share the same constitution-making process; they became independent first, and then adopted a constitution, without direct involvement by the British authorities. If you have any follow-up questions about these other cases, I'll take them separately.

In the main countries under consideration, the process of independence took a recurring pattern (there were variations, but this was the norm): it would begin with a pro-independence majority being elected to the colonial Legislature. By the decade before a country became independent, it would usually have a Legislative Assembly or Legislative Council that was mostly directly-elected, although often with a sprinkling of nominated or ex-officio official members. The newly-elected leader of the pro-independence majority would then formally indicate to the British that they wished to become independent. At this point in time, the British attitude was generally not to resist independence movements, but to seek to channel and influence the independence process, so as to create independent states that would be stable, Western-aligned, non-Communist, and favourable to British economic and strategic interests.

The British officials would then summon a Constitutional Conference, usually held in London, to which the majority party in the colonial Legislature, the opposition party in the colonial Legislature, and sometimes major interest groups or stakeholders (like white farmers in Kenya and the Catholic church in Malta), would be invited. The British - the Colonial Secretary and his staff - would open the Conference, facilitate it, and provide expert legal and technical assistance, as well as clerical support. They would sometimes intervene in the constitutional negotiations - sometimes to protect what were perceived as British interests, sometimes to protect religious or ethnic minorities who might otherwise have been overlooked by the majority, sometimes just to help the parties reach agreement. The actual negotiations, however, were mainly bilateral, between the government (majority) and opposition (minority) parties in the colonial Legislature.

The Conference would produce a report, containing a summary of the agreed constitution. An Independence Act would then be passed by the British Parliament, and the new constitution would be adopted, normally by an Order-in-Council made by the British Colonial Secretary under the authority of the Independence Act.

All this is background to the process of constitution-making. The choice of electoral system, like all other constitutional design choices, was worked out in these Constitutional Conferences. Unlike many constitution-building processes today, these were small, closed, elite-level gatherings.

Crucially, although these anti-imperialist nationalists wanted to end British rule, most of them came from an educated elite stratum of society that was familiar with, acculturated to, and frankly supportive of, the British way of ruling. Sir Ivor Jennings, who had a vital role in advising constitution-making processes across the Commonwealth, tells of encountering 'politicians as eloquent as Burke, and in Burke’s own language’ and lawyers ‘as ready to quote Coke’s Institutes or Blackstone’s Commentaries or the Law Reports as any young man in the Temple’.

Jennings describes - although in the form of a somewhat anonymised amalgam account from different countries ('Constitution-Making in Arcady', in Kumarasingham, H. (ed.) 'Constitution-Maker: Selected Writings of Sir Ivor Jennings', Cambridge University Press, 2014) meeting anti-colonialist leaders who had studied English constitutional law while in jail for seditious activities and 'End British Rule Now!' politicians who had studied at Oxford and were committed Anglophiles.

When it came to the constitutions of the newly independent states, other models and systems barely got a look in: what was wanted, pretty much across the board, was the British 'Westminster Model' of parliamentary democracy, suitably amended to the extent necessary in a post-colonial situation. This adaptation meant having a written constitution that would reflect the principles and institutions of the 'unwritten' British version, a judicially enforced bill of rights, and various independent commissions - an Electoral Commission, Boundaries Commission, Public Service Commission, Judicial Appointments Commission etc to insulate the non-partisan electoral, administrative and judicial systems from the influence of the Government. Other than that, what they wanted was the trust-and-parry of British-style democracy as it existed in the middle of the 20th century: with the Prime Minister and the Leader of the Opposition squaring off against each other; the Prime Minister able to set policy and be responsible at the next election for fulfilling his party's manifesto commitments, and the Leader of the Opposition able to scrutinise, criticise, and provide a credible alternative. Nothing else - nothing less - would do. If it was good enough for the British, it was good enough for colonies becoming independent from Britain. In the words of S. A. de Smith (1961), 'The last person to say 'British is best' will be an anti-imperialist nationalist on a desert island' (paraphrasing the quote from memory, but that's the gist of it).

More context: in the 1950s and 60s, the British way of doing democracy really did have an excellent reputation globally. Half the democracies of continental Europe collapsed in the inter-war period, and few of them were satisfactorily resurrected after the second world war. Spain and Portugal were dictatorships. Everywhere East of Berlin was under Soviet rule. Italy had an unstable and corrupt republic. France's fourth republic had died an anticlimactic death in 1958 and was replaced by a fifth republic headed by a charismatic general with sweeping powers whose democratic credentials were still unproven. West Germany was doing well, but had a terrible historical legacy to overcome. In all these cases, proportional representation had been blamed (unfairly, but mud sticks) for previous democratic failure or present democratic discontents. The Benelux and Scandinavian countries were decent and stable democracies with proportional systems, but they were not world powers and did not have much influence.

While many genuinely wanted what they saw as the benefits of British-style responsible two-party politics (with big, broad, mainstream parties alternating between Government and Opposition), nobody in the British colonies on the brink of independence was seriously contemplating and comparing the Swedish and the Dutch electoral systems - it just wasn't on the radar.

A few caveats. Firstly, it is worth pointing out that these constitution-makers were aware of the faults, as well as they saw it the benefits, of First Past the Post. They knew it wasn't good at representing minorities. They also knew that in many cases these countries lacked programmatic, ideological parties; parties were based on religion or ethnicity, resulting in low levels of electoral competition. They tried to counter-act this in various ways: through constitutional rights protecting minorities, through federalism or devolution that would allow territorially concentrated minorities to have a say over their own affairs, and by what might be called 'affirmative gerrymandering' - apportioning constituencies so that areas in which minority communities predominated - as was recommended by Jennings with regard to the Tamil community in Ceylon (it didn't really work out).

Secondly, the British were no strangers to proportional representation, especially Single Transferable Vote (STV). It existed in Ireland and for the Senate in Australia. It was used for the indirect elections for upper houses in India and South Africa. STV was used in Malta - where it had been introduced long before independence, and was retained at independence: crucially, before independence Malta had a multi-party system, although after independence it quickly morphed into a two party system. It was only in Guyana, that a radically different electoral system was experimented with, at the insistence of the British. This was a form of list proportional representation that was very unBritish but similar to that found in the Dutch Caribbean; in part this was a response to Guyana's ethnic heterogeneity, but as noted above this had not been a barrier to maintaining FPTP elsewhere; it was also an attempt to dilute the power of the majority party, which was seen as having pro-Communist sympathies.

So, in short, FPTP was rarely debated and largely taken for granted in the British decolonisation constitutions of the 1950s and 1960s - with an awareness of its shortcomings in some contexts, and with some attempts to overcome those shortcomings particularly in terms of ethnic representation, but also with a genuine and deep respect for the mid-20th century British system they sought to emulate.