Hmmm, my Wiki-sceptic meter is high on this one.
Friedman in British Carrier Aviation mentions that the 1951 rebuild plan was HMS Victorious then Implacable during 1953-55 and Indefatigable during 1954-57. Once refitted Implacable would replace Eagle in service to allow her to refit with receive steam catapults in 1956. Ark Royal commissioning in 1954 would make the fifth fleet carrier. In June 1952 the rebuild plan was halted by the Admiralty due to experience of rebuilding Victorious. So any major rebuild plans for Eagle were probably short-lived.
D.K. Brown in Rebuilding the Royal Navy also refers to the planned modernisation in 1955 costing £16.5 million taking 6 years which was rejected for a cheaper 'austere' £11 million 4-year refit, being approved in 1958 to allow operation of NA.39, Sea Vixens and P.177. He gives no details on the expensive scheme but it seems unlikely to have been too radical, given only £5 million was saved in trimming back the requirements, although its worth noting that this cheaper refit still gave 'A' standard in the carrier capability standards approved in October 1956 (listed in Friedman, A, B*, B, C, C(H), D, E, F; Eagle had been refitted to 'D' standard in 1954-55). Both Brown and Friedman agree that the 1958 refit was to 'A' and was still extensive, so we can only guess at what the extra £5 million and 2 years of added work might have been for. I can't see the Admiralty going back on their 1952 decision not to pursue structural rebuilds and I'm sure Brown would have been tempted to add more detail if something radical had been planned.
Victorious and Implacable were to be reboilered (cancelled for Victorious to save money and time) neither was to receive new turbines and it seems unlikely that Eagle would have required new turbines having only been completed in 1951 and having more powerful machinery than the earlier ships. Also Victorious had her flight deck lengthened 22ft. None of the proposals for the rebuilds of the older ships included hull length increases, probably for obvious reasons of cost and effort. Again, Eagle was already larger and had better hangar capacity. I think the 40ft extension on the Wiki page is actually meant to be flight deck extension rather than the hull. Without any accurate sources to back up those claims it sounds like misunderstanding to me, confusing reboilering with new engines and deck and hull lengths.