Sure. But that is not an alliance. It took two world wars to convince the US of the need to get into foreign entanglements.
There is no benefit to the US with closer ties to the UK. And why the UK? Why not Germany? The real money is in Europe and that is Germany's playground for the medium term. I get the feeling that the UK would be about to be on the receiving end of Sir Appleby's maxim about the balance of power in Europe with the US as the outsider. Perfidious America perhaps?
Either way decolonization is going to begin to bite the UK soon robbing the UK of the material resources needed to be a great power. Russia is going to rise, if only because it does have access to the material resources to be a great power and that will put Germany on notice. Somewhat ironic Germany will "win" then barely get the chance to enjoy it. And eventually one day China will get back on its feet because it always does.
There is no way, even with the most isolationist US possible, that the two Anglosphere empires cannot become rivals. The fact that they are built by financial supremacy and preserved by naval power is something that will bring things to a boil.
When? I don't know, perhaps if Britain stays out of the war the earnest US challenge may still not have happened, though I believe it does eventually.
How would it play out? The last time Britain and the US openly come to blows is 1812 and even then neither side had their heart in the war: the British still had their hands full with Napoleon in Spain when war was declared, whilst the northern US states and many of the merchant/business classes saw it as a potential disaster, both in military and business terms. Both sides then readily agreed to a settlement before New Orleans. There is a case that the rivalry is a cold war of sorts or war purely by business and trade. The US by 1914 has already succeeded by and large with the Munroe Doctrine and operates according to the free-trade Open Door policy, gaining dominance by opening up markets to US economic and industrial might as opposed to colonial or imperial ambition.
As for decolonisation, I am unsure whereabout this comes: if Britain stays out of the war then the military threats to her colonies from Germany/Russia (who I believe would still be too busy with each other after the war) wouldn't come until well after the war where Britain is still financially powerful if not dominant, with a rising Japan in the East to boot, if not others. The US is still on the other side of the world and although in OTL they were the ones to ultimately order Britain's dismantlement of the empire, it took 2 World Wars, with all the financial and economic damage those conflicts wrought on Britain in order to be in that position to finally finish her off. The fact that War Plan Red didn't take place when the US was as strong as it was and Britain as weak as it was, I think shows the level of caution with which US politicians approached Britain (or their own voters on the subject) even then.
Once past the initial crisis, I would suspect that domestic issues rear up to turn eyes away. If in here Grey is called out and resigns, and Asquith feels he must resign too, then Lloyd George and his clique gain the government and party. While there may be some split it should be less pronounced, but there is a scheduled election near on the horizon and the biggest issue is Ireland. Between the two I do wonder if the Liberals can secure another government or if the Conservatives can take their edge. My suspicion is that it is really close and we see some working coalition as the Irish PMs might lose their ability to keep the Liberals in power or wag them like a tail, Lloyd George seemed to work well with the Conservatives and they do not look eager to take full control and get their hands dirty. Ireland should be thorny enough to distract Britain from the losing war in Europe. But do we see some better resolution than civil war and independence for Ireland? And does Ireland indeed act as enough distraction to hold Britain too divided to commit to war as I opine? Ireland was the beginning of Empire, I think how it goes sets the tenor for how the Empire evolves, in OTL the Empire began a bloody and acrimonious dissolution from Ireland on, with something better here does Empire have a prettier future?
I have a few ideas but they are limited by my lack of knowledge about the parliamentary politicking of the time. Lloyd George and the other anti-war members of the cabinet were apparently blindsided on the 2nd of August by Asquith's revelation that the tories had openly backed the war and would happily coalesce with the pro-war liberals to achieve this. Grey actually used his resignation as a threat since if he and Asquith resigned, a coalition might well be formed in Parliament in support of war. After Grey got his way, he successfully convinced a good portion of Liberal MPs in Parliament with a speech the following day, with the day after that seeing Britain declare war.
What would have happened in Parliament had Lloyd George done as John Burns and John Morley had done - stand firm and forced Grey and Asquith's hand? Cabinet probably makes no decision/refuses to endorse Cambon's request for the RN's defence of the French coast (he apparently broke into tears when he met Grey before that cabinet meeting, something he used to try and emotionally convey the situation). Without this, Grey will have to resign, he may well not make his 3rd August speech and even if there is not a government properly in place (as I've mentioned before, I back Lloyd Geroge to succeed here if so) come the 4th of August then it would seem to me that Parliament would get a vote on the matter. Whether a Parliamentary majority for war can be formed, I truly do not know. Your guess is as good, maybe better than mine, though I believe there's every chance Kier Hardie, Ramsey McDonald and co. can get the noes to keep Britain out once and for all.
Other things to consider is, if Grey is gone (and but quick) after he fails to get his cabinet decision, who negotiates with Prince Lichnowsky (German Ambassador to Britain) the following day? PL was desperate to keep Britain out of the war, even going as far as to offer his country respecting Belgian neutrality in exchange for Britain's neutrality. Could a settlement be reached, or failing that, could the mere act of negotiating bring an extension to Germany's ultimatum to Belgium (You have until midnight on the 4th August to let us through or we're coming in any way)? What could/might be achieved, could it keep Britain out of the war?
Britain's next General Election had to be held at most 5 years after the previous one, meaning the government could remain in office until December 1915 if, by ASB, dodged the whole thing entirely. France by then would be beaten and I doubt even the tories could do anything about it.
Getting back to Ireland, I again have limited scope in what I can say for sure, if the Liberals cannot get a majority with the IPP, it may well have to find another partner to coalesce, maybe labour assuming they are asked to form the Government. Even with the tories in, the issue of Ireland doesn't spiral out of control or at least I find it much less likely. The Third Home Rule actually made it to Royal Ascent, only to be postponed until after the war, but I don't know whether this happens if Britain stays out. For me the THR bill won't bring peace, it will likely shift the unrest to the Protestant North, with all the complications of potential British Army mutinies, Ulster Volunteers and anything the Catholic south does. Yet, with no Easter Uprising I doubt Eamon De Valera, Michael Collins and Sinn Fein are the ones Britan has to deal with here, John Redmond and his IPP will likely be the main beneficiaries and the Dublin Parliament would eventually serve as a decent safety valve for many of the pressing issues the Irish had. I think there may have been talks in Parliament at the time about what I would have regarded as the best-but-not-perfect solution of a borderless political partition between North and South, with the Protestant counties under Direct Rule and Catholics given Home Rule, similar to now except that Southern Ireland is still part of the UK. It's a shame no quid-pro-quos involving Protestant emancipations/protections in return for Home Rule were considered AFAIK, which I think might have helped reduce the tensions.
The issues surrounding Ireland didn't stay in Ireland, they eventually transmitted themselves through activists etc. to places such as India and Africa, in this ATL where there is some resolution then there is little chance of this actually happening.