I did an estimate of population growth for the United Kingdom of Great Britain and Ireland without the wars. I did take into account a falling death rate that halves between 1920 and 1950 due to improvements in healthcare and sanitation. Also, though the birthrate falls, it does not do so as radically as on the continent. Ireland especially maintains a fairly high birthrate (as in OTL).
As for emigration, in 1913 alone, around 400,000 people emigrated from the UK (including Ireland). Around 1/2 of these went to Canada, just under 1/4 to the of the British Empire and around 20% to the USA. From Ireland, around 90% chose the United States as their destination. Emigration from Ireland peaked in the 1850s, declined a bit and rose during the 1880s, but went down until 1913 as economic conditions improved. However, without the war you'd have another 1.5 million Irish emigrating to the United States from 1913-2013.
As for emigration from England, Scotland and Wales, you would an additional number emigrating to following during the 1913-2013 period (keep in mind this assumes that the politicial status quo of 1913 remains in place). Also, unlike other countries in Europe, emigration will not necessarilly go down radically due to the fact that most of the receiving areas are English-speaking. This gives British middle-class immigrants an advantage in a world where borders are relatively open where they can seek job opportunies in Australia or Canada due to lower cost of living etc.
Additional Number of emigrants from Great Britain 1913-2013
1,500,000 to Canada
1,000,000 to Australia
800,000 to United States
700,000 to Rhodesias & Nyasaland
600,000 to Union of South Africa
300,000 to Kenya & Uganda
300,000 to New Zealand
250,000 to the rest of the British Empire
100,000 Elsewhere (1/2 to Argentina)
Population of Great Britain & Ireland
1921 44,796,000
1931 48,995,000
1941 52,015,000
1951 55,221,000
1961 59,211,000
1971 62,867,000
1981 66,743,000
1991 70,855,000
2001 74,772,000
2011 78,275,000
GDP in 2013 = $4.3 trillion