Friedman's "British Cruisers Two World Wars and After"
In the wake of the Abyssininian Crisis 1935/36 the RN began to plan to upgrade the fleet's AA armament. Part of that was to rearm the old C class cruisers and a number of V&W class destroyers and older sloops as convoy AA escorts. Friedman notes that:-
"In December 1936 the British government assured the Japanese and US governments, the other signitories of the 1930 London Treaty, that five of the 'C' class cruisers it was retaining would be converted into anti-aircraft ships, and that they would be scrapped by 1941. As of March 1937 plans called for taking four cruisers in hand during 1938 for completion by that December. The programme applied to six 'C' class cruisers and eight 'D' class cruisers, in addition to the two earlier conversions. Selected merchant ships would receive the set of weapons and fire controls as the converted 'C' class cruiser."
The retention of 5 C class cruisers, clearly with the agreement of the other parties, accounts for about 21,000 standard tons depending on what 5 ships were intended to be included. Maybe their rearming as AA ships with 4xtwin 4" was enough to remove them from being considered a threat by other parties.
There is also the question of the status of the Hawkins class as of Dec 1936 given that Britain could only retain 15 cruisers with guns larger than 6.1".
Raven & Roberts "British Cruisers of World War Two"
"Under the terms of the 1930 London naval Treaty, the Hawkins Class were due to be demilitarized by December 1936, as being additional to the number of cruisers armed with guns above 6.1in calibre allowed to the British Empire."
Article XVI (2) of the 1930 Treaty stated that they should be "disposed of gradually during the period eding on 31 December 1936", and Article XX (a) allowed Frobisher & Effingham, which were not then overage, to be disposed of by 31 December 1936.
So in 1932 Frobisher had become a cadet training ship with only 5x7.5" and 2x4". Then in 1936 Frobisher had her armament reduced to 1x4.7" and the 2xsubmerged TT "in compliance with the 1930 London Treaty" and continued her training ship role. Plans to refit her as in Effingham came to nothing and she was taken in hand to be rearmed in Sept 1939 after the outbreak of WW2. That process lasted until Dec 1941.
1937/38 saw Hawkins, Vindictive and Effingham demilitarized having all their 7.5" guns and above water TT removed.
Vindictive was converted to a cadet training ship after losing her inboard shafts and turbines and half her boilers which limited her speed to 24 knots. Her armament was then 2x4.7". She recommissioned in her new role in Sept 1937. Plans in 1939 to refit her along the lines of Effingham came to nothing and instead she became a repair ship in 1940.
Effingham, in reserve from 1935, was refitted 1937/39 as a light cruiser with 9x6" guns, 4x twin 4" and 3xquad 0.5". She also lost 2 of her boilers and had the funnels retrunked.
Finally Hawkins was also in reserve from 1935 and was due to be refitted as Effingham. But with the arrival of WW2 she was simply refitted and rearmed and put back into service in December 1940.
It is not clear to me by what means Britain was allowed to keep the Hawkins class in "demilitarised" form after 1936 but it happened. The removal of their main armament suggests at least an attempt to comply with the 1930 Treaty. They account for 39,440 standard tons of total cruiser tonnage.