There were 6 converted 1936-1940. 2 had been lost by the outbreak of war with Japan with another 3 lost in 1942.Its also worth remembering that a good number of the early RN light cruisers were being rearmed as AA cruisers with multiple 4in AA guns and modern LAA. A much better use for them than trying to pretend that they could still operate on the front line going toe to toe with other warships. In the Pacific where aircraft were so important this would only have increased their value.
In this role they performed well. IIRC, the RN vessel that was credited with the most aircraft kills during the war, was one of those converted light cruisers.
Coventry & Curlew were rearmed in 1936/37 as a reaction to the experience of the Med Fleet during the Abyssinian Crisis at the end of 1935. They lost all their 6" guns and TT. They gained 10 single 4" being removed from other cruisers being modernised at the time, controlled by 2 HACS Mk.III. They also had by 1939 one octuple pom-pom and 2 quad 0.5".
After that there were plans to convert more that at one point extended to the remaining 11 C class (with 4 twin 4" one quad pom-pom & 2 quad 0.5") and 8 D class (with 4 twin 4.5" + light AA). In the end only 4 other C class were taken in hand for conversion (Cairo, Carlisle, Curacao & Calcutta) before the outbreak of WW2 caused cancellation of the rest of the programme. Money was the reason for the delay, there being more important uses for the availble funds.
The next step was interest in the US 5"/38 and Mark 37 director in late 1940. Delhi was converted in the USA under Lend Lease from April 1941, returning to the fleet in early 1942. A second conversion was cancelled on US entry to the war.
Finally in mid-1942, after a number of the C class had already been lost Colombo & Caledon were taken in hand for conversion with 3 twin 4", 2 twin Hazemeyer Bofors and 6 twin 20mm. They didn't emerge until March and Dec 1943. Given the strains on British shipyards at the time, the resources expended on these two ships could have been better deployed elsewhere.
These ships lacked range for operations in the open waters of the Pacific.