I mean the military production during ww1 would be much higher than OTL
I know you did. I was only telling you where the idea came from.
However, British military production during World War One doesn't need to be much higher, because the British won anyway.
The way I did Scenario B2 for World War One the UK had twice the population, double the economy, but not double the armed forces in 1914. The British Army was twice the size of the real world in 1914, but it did not grow from 40 infantry divisions to 150 divisions in a straight doubling of OTL (when it grew from 20 to 75 infantry divisions). Instead it grew from 40 to 90 divisions. The Royal Navy was not double OTL because it did not need to be. The size of the battle fleet was determined by the size of the next two largest navies and the size of the trade protection force was determined by the size of the British merchant navy. As the rival navies were no larger in my timeline I only gave the battle fleet a few more battleships, armoured cruisers and destroyers. But because the British merchant navy was double the size of OTL in my timeline it had about 45 extra light, second class and third class cruisers, plus double the number of sloops, minesweepers and trawlers. Between 1914 and 1918 I doubled the number of sloops, minesweepers and trawlers that were built, but not the number of battleships, battle cruisers and light cruisers, with a moderate increase in the number of destroyers because they were dual purpose vessels.
IOTL the UK had a National Income of £2,241 million in the 1911-12 to 1913-14 years and a expenditure on servicing the National Debt of £24 million, which was 1.1% of National Income. In 1924-25 the National Income had increased to £4,035 million with £357.8 million spent on servicing the National Debt, which was 8.8% of National Income.
If the UK effort in Scenario B2 had been exactly doubled then in 1924-25 the National Income would have been £8,070 million with £715.6 million spent on servicing the National Debt, which was 8.8% of National Income. However, that was because doubled expenditure in the Great War doubles the National Debt.
However, if the effort was the same and circa the National Debt increases from £1.6 million to £8 billion (IOTL it increased from £800 million to £8 billion) so the cost of servicing the National Debt is £357.8 million in 1924-25, which is 4.4% of the National Income of £8,070 million. The National Debt does not increase to £8.8 billion because the tax revenue between 1914 and 1918 is double OTL.
Edit
According to the Wikipaedia article the UK and Colonies lost 750,000 to 880,000 military personnel and a further 1,675,000 were wounded.
IIRC you were talking about the UK population of 1914 being 50% larger. If the UK makes the same effort as OTL instead of increasing it by 50% about 400,000 extra men won't die and 800,000 won't be wounded. That's going to increase the size of the labour force after 1918 and it will help the British population grow faster after 1918 than it did IOTL.