Well part of it is that the RN never really stopped ordering large vessels all together. Never the same size, but the size of the ship is really secondary in many respects to its mission determining its complexity and attendant skill of manufacturing required. A giant oil tanker is relatively straight forward compared to a far smaller guided missile destroyer as an example.

In particular lets look at the Companies involved in the QE CV's. All of which have long histories well beyond the 20 year limit. We should also note some of the lineages all get jumbled because in the late 70's British shipyards were nationalized under the one organization known as British Shipbuilding but it started to spin off again in the mid 80's.

The first to spin off was known as VSEL which included the former Vickers-Armstrong yard at Barrow-in-Furness, and the equally historic Laird yard in Birkenhead. Then more recently the Vickers portion was acquired by BAE Systems who are now the prime contractor for the QE's. While 2 of the main sub contractors are Laird and A&P who at one time had bought the Laird yard at Birkenhead and some satellite yards. Both yards were very active in the first half of the 20th century, Vickers built everything from the SSN Dreadnought, to the IJN's Kongo, and made its bread on a multitude of submarines. While Laird built such vessels like Prince of Wales. Really one of the few names that has gone out of the actual ship building business which was in the early stages of the QE's design process was the old and famed Harland and Wolf, while the Royal Navy itself has also gotten out of the shipbuilding game reducing competition for what contracts there were/are. However final assembly for the QE's is being done at the RN base Rosyth.

So now that we have addressed at least what the yards involved had been doing and had the knowledge to do and what happened to them lets address your question in particular.

Basically they never really stopped for more than a few years in building large ships. Through the decades there was a steady drip of large ships, never quite the size of fleet carriers, but large and of similar scope.

Vickers(now BAE) built the carriers Hermes( now operated by India) and Invincible, while starting in the 90's built the Ocean and Albion class Amphibious Assault Ships. While Laird built the Ark Royal(newer one) and built a series of fleet replenishment ships for the RFA.

So in terms of complexity and level of demands there has never really been that large a gap when the RN wasn't procuring a ship of that scale. From the resumption of the post WW2 designs with construction dragging into the 50's, then in the 70's you had 2 carrier designs planned for. The larger CVA fleet carrier got scrapped but the smaller Invincible's would be built to take the place of Eagle and Ark Royal. And soon after the delivery of the last of that trio the modern set of Amphibs would be ordered.

So while the size and attendant need for more yard space and everything with that when you basically triple the tonnage brings headaches of its own the British Shipbuilding industry managed to survive on drips and dabs of work over the years on ships of similar complexity so as not to wither completely.