As I understand things the reasoning behind the Type 41 Leopard-class and Type 61 Salisbury-class was to use diesel engines, in part, to achieve the range needed as convoy and slow task force escorts. The Type 12 Whitby-class was meant to have almost the same range as designed but ran into problems, IIRC the clutch on the cruising turbine never worked properly, so ended up being comparatively short legged. One idea I saw made either on here or one of the other forums was what I mentally dubbed the 'Broader Beam Whitby' where the cruising turbine was fixed and the dimensions of the design expanded by a few feet and displacement a couple of hundred tons by increasing the amount of fuel to match the range of the diesel powered frigates. This would effectively give you a hull with similar dimensions to the broad beam Leander-class, it would also have the unforeseen benefits of increasing the weight carried lower down in the ship to help counterbalance later increases in top weight due to radar and similar systems, and possibly make it easier to operate helicopters in the future thanks to a bit of extra deck space.Also the operation of the Blackwoods, Salisburys and Leopards vs the Type 12s finally convinced their Lordships that quality was better than quantity and that a smaller fleet of better ships was the way forwards so other than hindsight something would have to occur to make them think this way!
Assuming that NOMISYRRUC's figures held up you would be able to replace the 4 Leopard-class frigates, 4 Salisbury-class frigates, and 4 Battle-class destroyer Air Detection Escort conversions with 12 Broader Beam Whitby-class frigates and have it be roughly cost neutral at least as far as construction costs. You would probably have to build two of them with diesel engines to tests things due to the 'Broken Back' idea, plus also to act as an experimental gas turbine conversion in place of HMS Exmouth if you decide not to build the Type 14 Blackwood-class, but it would still be a net improvement I would think overall.