Oh man, where to start. Well, there's not 100% agreement as to how exactly this came to be skewed as far as it was (per Anthony Christopher's article in Political Geography Quarterly 2, no 3 [1983] which I don't have to hand but may tomorrow) it's clear that this 'loading' of urban districts and 'unloading' of rural ones was legitimate by the terms given to Delimitation Commissions under the South Africa Act of 1909. Fortunately, the relevant sections appear in Florence Briand-Kyrik's 1953 MA thesis from UCT, "The Delimitation of Constituencies for the Union House of Assembly Under the South Africa Act." WARNING PDF DOWNLOAD. These Commissions were made of judges appointed from around the various provinces of the Union, and they might exert personal influence in regards to their views of electoral equity but seem to have done so lightly at most.

While Briand-Kyrik's conclusions and implicit viewpoints are definitely aged, it is relevant to your question for contemporary reasons as a result. It's both primary and secondary source, sort of, because this question of 'how could this juxtaposition exist?' was fairly widespread. Her analysis is a bit hard to read and runs on at times, but she does cover a lot of the various delimitations, which happened at intervals before elections and had an uneasy relationship with (white) migrancy, with the decennial census (supposed to be quinquennial), and so forth up to that time.

What's interesting is the terms of the delimitations, which people took to be 'objective' but really weren't. From Section 40 of the South Africa Act of 1909 (which Smuts couldn't upturn unilaterally--that's Constitutional-level amendin' work, there) given in Appendix 4 of the thesis (p12 of the PDF):

40.(1) For the purpose of such division as is in the last preceding section mentioned, the quota of each province shall be obtained by dividing the total number of voters in the province as ascertained at the last registration of voters by the number of members of the House of Assembly to be elected therein.

(2) Each province shall be divided into electoral divisions in such manner that each such division shall, subject to the provisions of subsection (3) of this section, contain a number of voters, as nearly as may be, equal to the quota of the province.

(3) The commission shall give due consideration to:-

(a) community or diversity of interests;

(b) means of communication;

(c) physical features;

(d) existing electoral boundaries;

(e) sparsity or density of population;

in such manner that, while taking the quota of voters as the basis of division, the Commissioners may, whenever they deem it necessary, depart therefrom, but in no case to any greater extent than fifteen per centum more or fifteen per centum less than the quota.

So, in the interests of subsection 40(3) and possibly avoiding gerrymandering that strict lines of 'equal population representation' in the manner more familiar to US readers might entail, they permitted the 'loading' of up to 15% either way (30% for certain exceptional cases after 1965!) but that 30% variability is easily enough to produce the results seen in 1948 and 1953. The 'quota' is the number of voters in the province divided by the number of divisions that province was deemed to have out of the total in the HoA (usually about 150, but varied because of a handful of special white representatives for Coloured and up to 1936 Black constituencies depending). If you add to this the flow of whites into the cities and the lag in registry, you get a further potential skew between the Delimitation Commission and the actual vote. In the case of 1953, South-West Africa had also been awarded six seats in the HoA, each of which had a per-elector count even lower than the smallest in the Union proper and its own Delimitation Commission.

The question that remains, then, is how this tilt in the delimitations existed and persisted, especially when it had become a fairly consistent feature? Subsection 40(3) is usually the culprit fingered here, and explanations vary--each Delimitation Commission had different weighting for the various considerations, and thus took slightly different views of the advisability of changes to electoral boundaries. Briand-Kyrik devotes much of a chapter (109 on in the thesis) to trying to follow this, and finds a significant degree of sacrosanctness put on the existing electoral boundaries in spite of clearly growing (white) urbanization, and on magisterial districts which had no connection to white population at all, among other factors. If you add to that the highly politicized nature of the National Party movement(s) during World War II, and the way that made eliminating Afrikaans-heavy representation into a lightning rod, you can see how trying to put a finger on the Delimitation Commission's scales would have fed right into the "Smuts is too cozy with the English / looking to gut segregation / etc" charges that had done damage in 1943 and would do even more in 1948. But really, Smuts didn't [necessarily] have the actual power to change how electoral divisions were apportioned, because it would have required an alteration of the South Africa Act's provisions on that point. I'm looking for information as to whether the United Party (or J. B. M. Hertzog's earlier Nats) even tried to alter Section 40; the bar for amendment was 2/3 and required the often-overlooked Senate as well as the more consequential House. Smuts never quite had that majority even after the 1943 election, falling just shy; Hertzog did under Fusion during the Depression, but in 1939 with the falling-out over the question of neutrality that majority split, and [edited text and strikethrough to reflect correction below; the explanation is clearly more complicated in light of the actual amendment of section 40 and the lower bar for amendment of most sections of the Act including 40.] Hertzog had been the beneficiary of this imbalance anyhow so he had no need to alter it.

As for 1953, carry the ball further and add the 6 new votes for South-West Africa to the NP total as 'reliable seats.' That, along with the momentum of the above Commissions, is what produces a huge Parliamentary majority from a small electoral one.

[edit @ 3 min: link didn't work, oops; edit @ 11 min: formatting fail also]

The other question you asked is about acquiescence. Well, there was outcry, but not necessarily from most of the white electorate. If you look at the development of the ANC Youth League and the progressive movement of the [ed: other opposition, incl African, Indian, Coloured, and some across color lines] organizations towards working together--despite the revolt of 1949 against Dr. Xuma by the Youth League--you can see perhaps the most consequential non-acquiescence that reached a crescendo in the Defiance Campaign which sought to overwhelm the ability of the fledgling apartheid regime of Malan to enforce spatial restrictions and the new pass law. Of course, this broke down amidst the attack on Congress Alliance leadership and produced violence that helped Malan in 1953, but initially they'd hoped for broader support from white liberals. Among the electorate, however, I'm not as familiar with the broadsides against this non-representative outcome; Smuts died in 1950, and they had no legal leg to stand on in any case. Perhaps someone else can speak to this, or one of the digital collections (overcoming apartheid at Michigan State, for example) may include such treatises.

[added: As for why a popular majority of voters went for the Nats in 1953, look at the fear stoked by the Defiance Campaign, which they exploited; the addition of SW Africa's whites to the rolls; the lack of compelling UP leadership (Smuts died in 1950); and of course the Cold War and their positioning around the Suppression of Communism Act and so forth.]