I've seen the 5x15"/42 suggestion on here too, but I'm not convinced. It would basically be merging the Iron Duke and QE design philosophies, when part of the reason for the QE's had been a deliberate shift toward a different design concept. Part of the point in being armed with 15" guns was to have fewer harder hitting guns to maintain or increase the ships' total firepower while freeing up tonnage for other purposes, like the power plant for a higher maximum speed. Building a 5x15" ship would be a reversion away from that strategy, as it would either mean eliminating the "fast" part of "fast battleship" or a substantial increase in displacement and therefore cost. And all when the QE's were still better than any of their competition. In my opinion, the 1915 program would consist of a "refined" QE- faster, better lay out, essentially ironing out all of the flaws in the original QE's and tinkering with the design to be a more perfect fit to the fast battleship role. It's worth remembering here that the naval program is going to be heavily dependent on the political situation. Part of the deal Churchill struck with Lloyd George for the increase in the 1914 naval estimate was a substantial reduction in the 1915 and 1916 ones. I think that indicates that the Royal Navy will eschew an expensive new design, especially one which promises to either sacrifice capability, but still cost more than the QE's, or be even more expensive for not all that much gain. Additionally, the Royal Navy will be looking for ships that can be stretched further in terms of utility. Basically they need better value for their money, because they're facing a shortage in the number of ships available for non-home deployment due to the failure of the Canadian Naval Bill. To me, all of that will drive a desire to improve and enhance a good design they already have into an excellent one. However, all of that is dependent on the political situation keeping steady. Any number of things could happen to change it such as the Germans deciding to make another run at surpassing the British fleet and laying down a lot of ships or better ships, or conflict over Home Rule in Ulster, or news of Russia's considered 16" designs gets out and public opinion forces the government to fund a bigger program and purchase more powerful units, or the same thing could happen with Brazil, depending on if the the battleship they were rumored to be looking for in 1914 gets ordered and what it looks like. Or the opposite might happen and convince the government that the 1915 program is uneccesarily strong or large. The point being, the 1915 program depends on a number of things that could go either direction.
Now, that said, I think we can see a few likely long term trends in Britain's naval programs. First, there will be a shift away from huge numbers of battleships to fewer more individually capable ships and a greater emphasis on light units to support them. Capital ships had been increasing in cost at an astronomical rate, in the past couple of years so the government would be eager to try and minimize those increases. As an example, the move to 15" gus had increased the price of capital ships by about 30%. That's twice the increase in price caused by the move from 13.5" to 15". So it will be clear to just about everyone involved that the trend won't be changing any time soon without a sea change (pun most certainly intended) in ship design. That incentives ways to maximize the military capability of the fleet for the money spent. Which means building more light and supporting units to buttress the epensive battleships and developing techniques to allow greater mutual support between fleet elements. That will make the whole fleet not only more effective, but more cost efficient. So I think we'd see significantly more money going toward cruisers, destroyers, and submarines. For the former, I think that would take the form of many more light cruisers and efforts to push the capabilities of armoured cruisers. Maybe an early development of the proto-heavy cruiser? For the latter, it would take the form of substantially more in general, but especially on developing types of submarines that could function in some way work as an arm of the main fleet. Unfortunately, that will likely lead to an alt-K-class. Though perhaps someone will think of a better alternative. Lastly, I think there will be very strong interest in utilizing aircraft at sea from the Royal Navy. Their most pressing problem is having a worldwide empire and never enough ships to go around. Aircraft help solve that by giving the units equipped with them the ability to scout a much larger area, and acquire the information faster. That means a given number of ships can cover a greater area, and improves the navy's efficiency. However, aircraft also help with the expected problem of facing the German fleet in the North Sea because it aides in the detection of the enemy ships, which is a great help to the Grand Fleet effectively maneuvring and intercepting. Lastly, I'd just like to buttress my contention that the Royal Navy would move toward combining captial ships and supporting units by noting that in 1914, the Navy planned to disband the Battlecruiser Force and create a number of "Scouting Forces" that would consist of a battlecruiser and a number of smaller ships that would each act as a distinct unit.