Exactly the opposite in my opinion.
In the period from about 1950 to about 1980 it was more cost effective for the Royal Navy to buy new ships than modernise existing ships. This is because hulls and machinery are cheap while weapons, radars, sonars and computers are expensive.
IMHO it was the money spent to complete Hermes, Tiger, Lion and Blake and the rebuild of Victorious that was wasted. It would have been better to have spent the money on new aircraft carriers.
Comparisons with the American legacy fleet ships are misleading because they tended to be bigger than equivalent British ships, which made it easier to modernise them. They also had hidden advantages like using electric power for gun mountings rather than hydraulic power, AC electrical systems instead of DC and better accommodation for their crews than war built British ships.
I'd like to see examples of this savings. It always turned out to be untrue , when I dug into it. The aborting the cruisers and carriers is a good example. Vicky cost £30 million spread over the 1950s, while completing the Hermes expended £11 million from late 1940s through first half of 1950s. The Tiger class completion was £19 million spent over the same period as Vicky, plus further £19 million in the 1960s to convert the Tiger & Blake into more useful Helicopter ships.
Through the 1950s that's about £57 million invested in these warships . If they could build a large deck carrier , the CV-52 was estimated at £105 million just to build one such ship and that says nothing of the jets needed to fly off it. Those would more than double the projected cost and operating budgets. Now it just so happens the RN had over £60 million invested in the SEA SLUG development through the 1950s plus another £90 million developing the failed Mk 20 torpedo. Cancel all that lot and you might just have enough to buy two CV-52 Carriers, but no DDG/CG to escort them.
But don't fret , you could still cancel all the useless frigates.
12 Blackwood total £20 million
4 Salisbury total £13 million
6 Whitby total £17 million
4 Leopard total £20 million
That's roughly £70 million ...not enough for another CV-52 but it could fund the SEA SLUG development through the 1950s or buy 70 more naval jet fighters for these carriers. Don't worry the cost of refurbished WW-II DD should only be £ ¾ to 1.5 million each.