The Royal Navy was first on the chopping block. What happened next was undoubtedly Mountbatten's finest hour and what he achieved in late 1956 and early 1957 gains him the honor of being the finest professional head of the Royal Navy of the 20th century. Mountbatten had the wisdom and common sense to realize that times had changes and those who did not go with the tide would be swept away by it. Mountbatten looked through the defense policy, picked out those areas that the Royal Navy could do (and could make a good case should do) and offered to scrap everything else. Those roles were firstly protecting the sealanes to the UK - primarily against submarines but also against long range air attack. The first required frigates, the second carriers. Then he took the "defending UK interests outside NATO. Mountbatten pointed out there were only two ways of doing this. One was station army garrisons at every point of possible contention. the other was to use a mobile mix of carriers and amphibious troops to intervene where trouble threatened. He pointed out that such trouble did not flare up without warning but took time to come to the boil. Therefore good intelligence was also needed. Finally Mountbatten made a grab for the strategic attack role. He started by schmoozing Rickover into handing over details of the US nuclear submarine and Polaris programs. From that he was able to show Duncan Sandys that the stategic strike role could be taken over by nuclear-powered submarines carrying the new Polaris missile. Everything else not needed for this program; the cruisers, the battleships, the huge force of old, ineffective escorts etc etc would be scrapped. The results would be a much smaller, leaner but more effective Royal Navy. Sandys was converted. He had gone into the process bitterly opposed to the RN carrier fleet and naval forces in general. He came out an enthusiastic convert and supporter of the Navy.
Next was the Army. Montgomery was the antithesis of Mountbatten. He had nothing but contempt for Sandys and no regard whatsoever for the new orientation of defense. His contribution was that the Army knew what it had to do, was the way he wanted it, and that was the end of the matter so there. His policy documents made no concession to the political and financial realities that were breaking nor to the requirements of the Cold War. What little strategic vision they possessed was basically that World War III would take up where WW2 had ended. The rest of the Army would go about its business garrisoning various parts of the Empire. The result was the institution of the trip-wire strategy. On the basis of the Army's own submissions, it could not make a reasonable contribution to defending Europe on the basis of the resources available. Therefore its function was cut back to a trip wire that would hold the line just long enough to allow a final attempt to persuade the enemy to abandon the attack or face nuclear weapons. Even that required the legions to return home. There would be no British troops available for far-flung garrisons. What wasn't in Europe would be the UK garrison
That left the RAF. This is the only part of The Way Forward (the official name of the 1957 Sandys White Paper) that gets talked about, primarily due to the effects of the RAF propaganda machine. Again, some background is necessary. There was no doubt that the defense of the UK against air attack would fall to the RAF but how were they best to do that? Here its necessary to remember that the UK aircraft industry had a long history of delivering aircraft that were years late and never performed as well as they were supposed to. Furthermore all the investment made in the aircraft industry since 1945 had been wasted on a clutch of competing prototypes that had always been that little bit too late to be viable. There was no prospect of that changing unless the aircraft industry was totally reorganized. The RAF showed no signs of recognizng these limitations; their proposals rested on more fighters, more bombers. Duncan Sandys had been primed by his meetings with the Navy. He knew the key question to ask. Missiles.
Could the fighter defenses proposed fend off ballistic missile attack? No. Could the fighters get off the ground fast enough to avoid being destroyed by ballistic missile attack? No. Could fighters respond fast enough against bombers to prevent them launching long-range supersonic cruise missiles? No. Any good reason why we should build fighters then? Errrrrr - they look nice? Sandys knew that the USSR was investing heavily in ballistic missiles of various types targeted on Europe. He knew that they were building new generations of missile-carrying bombers. The fighters operated by the RAF and those supposed to enetr service were great for fighting the Battle of Britain but that was of no significance. they couldn't protect the UK against the most likely threats so what was the point of having them. On the other hand missiles could. They could respond instantly and offered the chance of defending against missiles. Sandys was well aware of what was going on in the USA and where the fabulous Nike system was going. there was a threat, missiles could meet it, fighters couldn't. Bye-bye fighters. There would, of course be an interim gap so that was filled by an interim fighter. Hello Lightning. A side benefit was that none of the proposed missiles would have been built by the existing aircraft industry (some of the names were the same but the design teams were not). So they didn't have a demonstrated record of failure.
The RAF wanted to keep strategic attack with bombers. Could bombers, existing or planned penetrate the missile-based air defenses of the USSR projected for the late 1960s (assuming they were at least equal to Nike)? No. Bye-bye bombers. Replace them with missiles. If the land-based missiles failed go with the Navy's Polaris. As an interim there was this thing called Skybolt.
So viewed in the context of the times, Sandys had the right answers to the right questions. In reality he did a good job. When he left office in 1959 he had placed Britain's defense forces on a secure strategic, administrative and financial base. If, as the question presumes, his White Paper had been abandoned, the results would almost certainly have been the total collapse of the UK armed forces and the bankruptcy of the UK. The British just couldn't have gone on the way they were where the defense forces were consuming more than 10 percent of GNP (and not getting a proportionate return on that money).