Looking at the promos for the upcoming games, I see that in all instances (where I recognize the national flag) the flags for the teams are represented by the country’s flag. All except England’s, which is a red cross on a white background instead of the familiar Union Jack. Why?
Because the Union Flag represents Britain, the cross of St. George represents England.
Because that is England’s flag. Unlike other states, the UK is represented in soccer by its four constituent nations. There are historical reasons for that, but others can fill in the gaps. So each of those constituent nations uses its own national flag: England with the Cross of St. George, Scotland with the Cross of St. Andrew, Wales with The Red Dragon, and Northern Ireland with whatever got cobbled together to not try to offend both the Republicans and the Unionists.
In short, the United States is facing England tomorrow, not the United Kingdom of Great Britain and Northern Ireland.
The question has been answered, but to fill in a bit of the background, the England flag phenomenon is a relatively recent thing. If you look back at coverage of England fans in tournaments in the 80s and earlier, the red, white and blue of the Union Jack/Flag is much more in evidence.
The phenomenon of the English red cross replacing the Union Jack in popular culture probably goes back to the European Championship of 1996, which was held in England. Before then, ostentatious patriotic flag-waving was stained by association with football hooligans and thuggish organisations such as the National Front, and they preferred the Union Jack. Euro '96 reclaimed the English flag for normal people. Since then, it has been everywhere during football tournaments. You can’t drive half a mile at the moment without seeing an England flag fluttering from a passing car’s window.
Myself, I still feel a little uneasy at any kind of flag-waving, but the displays of English flags that you see during football tournaments are seen as innocent and unthreatening expressions of patrotism.
…and that really has little to do with the OP, so sorry about that.
As others have said, the English football team represents England, not the whole of Britain, which includes Scotland, Wales and Northern Ireland, all of whom have their own national teams that are eligible to compete in international tournaments such as the World Cup.
The Union Jack/Flag is the flag of Britain, and was constructed by overlaying the red-on-white vertical cross of England, the diagonal white-on-blue cross of Scotland, and later the diagonal red-on-white cross of St. Patrick, for Ireland and then just Northern Ireland. As for Wales, it has its own flag, but has been an English principality for so long that in many matters it tends to get subsumed into “England & Wales”. So there’s no explicit representation of Wales on the British flag.
I saw some Americans commenting that they would beat Britain, the UK etc in the footie … um … definitely not … neither Britain or the UK are playing. 
Well explained above.
My only nitpick is that Britain is not the nation, it is an island: (Great) Britain, which contains England, Wales and Scotland. The nation is the UK (the United Kingdom of Great Britain and Northern Ireland). Northern Ireland is not part of Britain, apart from the confusing fact that the nationality of citizens of the UK is ‘British’.
My understanding is that the UK government does actually recognise the term “Britain” as being synonymous with “UK”, including Northern Ireland regardless of geographical exactitude, whereas “Great Britain” is not used in such contexts and is, strictly speaking, just the name of the largest island. I thought this distinction had come up in previous threads on the subject, but there have been so damn many of them.
I’ve also noticed the White Ensign, the Royal Navy’s flag, used by English soccer fans recently, sometimes with wording superimposed: White Ensign - Wikipedia
So, how come England’s star is pale silver and not gold? I had a hard time spotting it and even thought it wasn’t there for a while.
Aesthetics.
Purists will (correctly) tell you that, unless flown from a Naval vessel, it is the Union Flag, not the Union Jack.
Oft-repeated, but actually open to debate. Nobody seems to be completely sure where the term “Union Jack” comes from. It probably is because it was originally a maritime flag, but that does not in itself mean that it is wrong to call it a “jack” when it is flying on land.
*The origins of the “jack” in union jack could derive from its maritime associations - a jack is a national flag flown by warships - but other theories are that it comes from the “jack-et” worn by soldiers or from the Latin or French form of James: Jacobus or Jacques.
Whatever the real explanation, the debate about what to call the flag when it is flown on land - union jack or union flag - rumbles on.*