There are number issues with the design.
From the Cruisers of 1960 (designed in 1948-49) onwards the British Cruiser designs were supposed to have guns that were able to train 360 degrees in all elevations without colliding with the superstructure or each other. The rapid training speeds required to engage aircraft (38 degrees per second for the 6in, 60 degrees per second for the 3in) mean that they will build up considerable momentum. If they have to stop clear of superstructure, they have to slow down well before that point degrading performance. Individual mountings will also be controlled by their own MRS director, hence will be firing at different targets. As such they must not interfere with each other.
The 3"/70 QF Mk N1 mountings cannot be placed so close together. The previous point about 360 degree traverse still stands, and each mounting has a muzzle sweep of 21ft. Each mounting also requires a 400 square foot magazine in the form of a "bottling plant" underneath the mounting. To have an idea of what I mean see the following:http://collections.dockmuseum.org.uk/mw ... 4;type=101
, http://collections.dockmuseum.org.uk/mw ... 8;type=101
and http://collections.dockmuseum.org.uk/mw ... 1;type=101
. They cannot be placed so together. Depending on the beam of your ship, you also be unable to significant amounts of superstructure on the centerline, since the combined muzzle sweep of two 3 inch mountings will prevent the use of more than 42 feet of beam. You may have to keep superstructure to a minimum, and increase volume within the the hull to compensate, like the Cruisers of 1960 and the 1949-54 Cruiser-Destroyer designs.
Radar and other sensors: Is not all that bad. You have an air search radar (Type 960) and a Target Indication Radar (Type 293). Unfortunately when it comes to surface search radars (Type 277) although you have chosen the correct type, the placement is off.
That said, given the period of this ships, a slightly later generation radars are probably a better fit. The number of mountings and directors your design has will considerably exceed the number of targets the Type 293 and it's associated Gunnery Direction System 2 can cope with. The Type 992 radar, and it's associated Gunnery Direction System 3 offered the ability to target 8 separate contacts, each with three weapons or directors, for a total of 24 directors and mounts. This is a much better fit for your ship.
As for surface search radars, I suggest doing away with all of the Type 277 radars, with the exception of the one on the mainmast, and add a Type 974 radar on the foremast. This appeared on both the Tiger class and on the 1949-54 Cruiser-Destroyer series.
Fighter Direction (this is a suggestion, not a recommendation): Given your ship's role as a task force escort, a fighter direction is likely to be a requirement. There are several approaches to this. The existing Type 960 and 277 combination will offer limited air search and heightfinding capabilities.
To improve on this however 1-2 Type 980/981 or Type 982/983 combinations will be required. The Type 277 can be disposed of, but the 2-4 radars required will consume a large amount of centerline space, which will already be limited by the requirements for the armament, directors, masts and funnels.
Alternatively 1-2 Type 984 3D radars are also an option, which have the benefit of getting rid of the need for both the Type 960 and Type 277. Sketches IV and V of the 1960 Cruiser schemes, along with Design II of the 1951 Cruiser Destroyer design series had two Type 984s. However two Type 984 will likely interfere with each other, and none of the Aircraft Carriers that were equipped with it carried more than one. A later Cruiser destroyer design study, and the GW series of Missile Cruisers which culminated in GW96A were designed with one Type 984.
Sonar: This ship will not be performing anti-submarine operations, but around this time British Cruiser and Carrier designs were provided with a Type 176 torpedo warning set. I suggest you do the same.
Masts: The mast also need work. The radars are heavy enough to the point that you will need lattice masts to carry them. If you are limited by centerline space, combine them with the funnels to create macks (which you have already appeared to have done). That said, they would look more like the foremast and funnel of the Daring class destroyers (1949) or that of Sketches III, IV and V of the Cruisers of 1960 series.
Directors: The LRS-1 and MRS-3 directors are the correct choice for this ship, given its role and the period it is constructed in. That said, make sure they don't mask each other, and make sure that they similar fields of view to the mountings they control.
I may be wrong but the FV-1/Type 91 jammer antennas below the starfish on both the fore and mainmast are obsolete by this point, although if you want to keep, no more than 4 (two port and starboard) on the mainmast only should suffice. The HF/DF Antenna is also obsolete, and should be replaced by a UA-3 Porker Antenna (see the British Parts sheet).
By this point the Royal Navy did not have any aboard cruisers. Aircraft and associated catapults were removed from 1943 onwards.
That said, of you still want to use aircraft in any of your future designs (although not this one), from the Towns onwards, the Royal Navy used fixed athwartship catapults on their cruisers, not rotating ones. A 4 aircraft hangar is also too large for a cruiser, with British cruisers having hangar space for no more than two. The only aviation facilities that this ship is likely to have is a landing spot aft for a Westland Dragonfly.
Boats: British cruisers were expected to operate with considerable autonomy, and as such had considerable boat complements. Unfortunately, in terms of both quantity and type, this is outside the boundaries of my knowledge, but I would suggest at least a pair of whalers (port and starboard, so we would only see one) and a couple of Motor Launches. The sketches for the Cruisers of 1960 show only 3-4 boats, but the official Admiralty model for the unbuilt GW96A (designed about 8 years later) shows considerably more:https://collections.rmg.co.uk/collectio ... 67652.html