This has been a long and storied debate in the UK. By and large, everyone is against it, but while for the English it's mostly just a case of "we don't want to play with them" for Scotland, Wales and Northern Ireland it's something deeper. You have to understand that the only reason that the four different UK "home nations" have their own teams is because of the historical connection - because we are the first four countries in the world to have had FAs and leagues and we formulated the rules of the game. Even today the IFAB (the board which votes on rule changes) is constituted of four FIFA members and the four British FAs, meaning that the UK gets equal weighting with all of the rest of the world combined on whether to make any changes to the laws of the game.
Thing is, FIFA doesn't like this. They've long had the opinion that there should be one FA, one league system and one national team per country, and that the UK shouldn't have its four FAs any more. There have long been accusations of FIFA being deliberately anti-UK because they want to get rid of the influence the UK has. The problem is that to get rid of the four FAs would do little damage to the English league system, but it would utterly wreck the Scottish, Welsh and Northern Irish leagues. Virtually none of their teams are of any standard at all - I'm being serious when I say that probably only two or three teams from the top Scottish, Welsh and Northern Irish divisions would be able to play even at Conference level (tier 5) in the English leagues - and they're all Scottish - and the only way that the four leagues could potentially reorganise would be for Scotland, Wales and Northern Ireland to join the English system as regional leagues, which would basically banish all of their clubs from Europe for All Time and would drive most of their clubs and leagues out of business as they lost their TV broadcasting deals and no longer playing at the top level meant all the money in the league bled out into the English game.
In other words, it would be the death knell for Scottish, Welsh and Northern Irish football. They already despise us enough, we don't need the kind of endless hatred they would have for England if that ever happened sitting over us.
At the moment, FIFA can't do anything about it because there would be too violent a backlash - and after all, it's not as if the UK having four national teams and national leagues is allowing us to dominate world football, so the damage to FIFA is minimal. However, there is a strong suspicion - one that is probably correct - that FIFA is just waiting for the UK to slip up before pouncing and demanding "merge your FAs or be expelled from FIFA", and for that reason the other UK countries are unwilling to make even token commitments to cooperation. I mean, heck, Scotland and Northern Ireland take the threat so seriously that they told their players before the 2012 Olympics (when the UK was required to send a UK team) that any player who accepted a call-up to the GB football team would be banned from playing for their country ever again.
There's simply too much riding on it for this to ever happen, unless it was forced on us.
