In my opinion, it would be the death knell for the United Kingdom. If the Conservatives come to power as a result of the Home Rule Crisis when the volunteer armies of Ireland have already been formed and home rule in Ireland hasn't been granted, it will be a very vicious war of Independence there with not just Sinn Fein but the Redmondites also waging war against Tory Britain. Imagine that, open warfare in Ireland between the Irish Volunteers and the British Armed Forces during the First World War.
Liberal Non-conformist Wales would be much less enthusiastic about fighting the war as it wouldn't be their government doing it. And if the Conservatives are agressive enough to enter the war before the invasion of Belgium, Liberal England might be much less enthusiastic. Conscription would be met by a hostile reaction among both liberals and the working classes and worst case scenario, if exacerbated by the war in Ireland, spark a nationalist war in Wales.
So you have England fighting a war that is not about small nations and at the same time there is civil war in its' back yard.
In my opinion, Britain would be defeated and Ireland, if not Wales would also become independent.
The Tory Party would be a gonner and the Liberals will become rUK's centre-right party.