Unfortunately the POD is 1914. Having said that the Edwardian UK didn't need a bigger army in peacetime, it needed a better one.
A good place to start would be the Territorial Force. IOTL it was still equipped with Boer War vintage weapons and it's formations weren't organised on the same pattern as the Regular Army. For example its field artillery batteries had 4 guns instead of 6.
If the 14 infantry divisions in the TF were organised on the same pattern and had the same equipment as the 6 Regular Army infantry divisions that would at least have given the British Army a bigger gun and ammunition making industry plus larger stocks of modern artillery shells at the start of World War II. That would have relieved the shell shortage somewhat and allowed the munitions industry expand at a faster rate after war was declared.
I don't know if its true, but I did read in one book that Lord Haldane wanted a TF of 28 divisions but was only able to get the Cabinet to approve 14. I'm not sure that enough men could have been recruited in peacetime if the money had been made available, but what might be possible is that the 20 home based infantry divisions (6 regular and 14 TF) could be given a 100% reserve of modern equipment to replace losses while industry was mobilised and to facilitate rapid expansion in an emergency.
Whether or not that would shorten the war is another matter.
Which is nice from a gear head persepctive but the admirality would much rather have won the war.
The BEF fought well above its weight and grew to a massive force, without committing to fighting in France and keeping France afloat financially (and it was not just a question of gold here) France is not holding back the Germans, if France falls Russia is certainly not lasting any longer than OTL so Germany gets to do what it wants to Europe which certainly is not what Britain wants. So a few ships and some worthless colonies vs losing two major allies and facing a hostile continent that would have the resources to compete in a naval arms race that Britain needs to not only win but win well enough to also defend the empire at the same time. OTL it could not do this with Japan's rise. ITTL it certainly cannot do this with Germany not being badly stunted in the naval department.
The R class was ordered under the 1913-14 Navy Estimates, which ended on 31st March 1914, which unfortunately is before the POD.
Similarly the your Super QE would be better than the OTL Hood, but it would not be completed until after the war ended and therefore didn't contribute to winning the war. IIRC Hood cost £6 million to build and the £860,000 was spent on her 3 sisters before they were cancelled. So either the money shouldn't be spent at all or the money, labour and steel used to build more tanks.
I did consider including not building the Hood class in Post No. 91.
Conscription was a difficult step for Britain - it was just so......un-British.
However I do agree - the problem with relying on an all volunteer force is that the military is reliant on using those men and those men often have chosen the Regiment of choice further reducing the army's ability to reinforce / expand certain units.
Conscription however serves several purposes - the most important and not immediately apparent one - is that it keeps skilled workers where they are needed - this was done straight away in the years leading up to WW2 when conscription was reintroduced.
The other main advantage of conscription is that it allows the military (in principle) more leeway in placing men where tehy are needed and where their skills are of greater use in particular jobs and regiments etc
Lastly it allows control over the rate of call up - at the beginning of WW1 volunteers spent months living in tent cities drilling in civvies with Broom sticks because there was no way to equip them - the country was still struggling to adapt its industry to a war one - better to have left them where they were till they could be properly inducted, equipped and housed etc.
Overall, I think there are several steps to do:
1) Take a firmer and clearer position over Belgium neutrality to force the German to abandon Schlieffen Plan. The French industrial heartland would be in tact, thus reducing the
British financing costs for France by at least more than half, and the French would be self sufficient for quite long. But the British would be denied war entry for months.
2) Trading with both sides but skewed towards the Entente to accumulate cash for military buildup. Require the French to pay in gold if they run out of cash. Sending merchant ships carrying supplies to Russia via both Dardanelles and Baltic, this may help create a viable casus belli if they are sunk or robbed. But I expect that the American would also want to sell to France and Russia, so the German will not want to provoke both the UK and the US at the same time. Also buying up spare products in US machinery market, use most of them for industrial buildup and sell some to France at a slightly higher margin, and some to Germany at a profit margin of over 10 to 1. Indirectly drain Germany by exporting non contraband goods like clothes, footwear or processed food to Low and Nordic countries, and these goods would be reexported to Germany at higher prices (if selling directly to Germany and Austria, then charge sky high prices, force them pay in gold if possible).
3) Completing the Iron Duke class and at least one of the QE class.
4) Gearing up war industries like OTL, also send experts, observers and volunteers to France to learn about the tactics and weapons (such as optical instruments, chemical weapons, high explosive shells, aircraft, trenches or tanks). I expect the industrial buildup would be better than OTL because of more skilled labour retained and more money invested (e.g.
the money which was spent on building French factories and keeping them float OTL), and this would lead to a decision which involves producing weapons before recruiting troops. No conscription on industrial workers.
5) Baltic Project: rule out the amphibious assault and the use of Grand Fleet, but carry out the first phase of the project: the large scale construction of destroyers, minelayers, submarines, cruisers...These ships would be very beneficial for ASW and blockade. Or they can be used to raid and harass Germany to lure the HSF out. Since Belgium ports are not occupied, the submarine threat is much lower. Greater and more aggresive use of mines on the two exit routes for Germany from Baltic to North Sea.
6) Banning German warships from entering home water and the Channel (a potential casus belli). Also, laying Dover barrage like OTL.
7) Planning for a shore bombardment on Dardanelles to tie up a portion of Ottoman strength their AND a landing on Alexandretta to cut the empire into 2 parts. Forget Salonika. This would be success, thus Fisher would still in charge. Overall, although he has some crazy ideas, he is very good at accelerating ship construction progress, which means faster naval expansion. Also, with him, I also expect new BB and BC generation with stronger guns to be developed just some time after Jutland without delays, much earlier than OTL. A guy like fisher would be very likely to scrap Admiral class and go straight to G3.
8) Forming a secret pact with Italy, maybe promise new territories or some economic benefits like discounting selling coal price, to keep them from joining war on Germany's side or better, persuade them to join Entente when Britain goes to war.
9) Developing aircraft carriers. Only them can provide a viable mean to raid on HSF at their bases.