I think the reason that Ireland, Scotland and Wales have apparently stronger "identities" is because they were "conquered nations" by the English so those who wanted to keep their identities have as it were an uphill battle and the flag therefore expresses those efforts.
Indeed, although of course it doesnt go for every case, it is often nations that had to "fight" or still do have to fight for their identity or very existence that have the strongest feelings about flags.
Even the USA, remember, had to fight the English for their nationhood.
It's been a very long time since England just as England had to hold fast to an ID and therefore their flag.
We were the conquerers: indeed, we tried to plant our or the Union Jack flag around the world. the fall of our Empire and the gradual erosion of the Commonwealth still has meant we have not been actually attacked. Really, what Empire did was to give our flags a different set of meanings that resided in being "on top". Therefore a complex relationship between the Union Jack and England flags.
This doesnt mean to say we should don't celebrate today, but it does show why, compared with other nations, its meaning is somewhat diffuse, unless it's a footie match. Because we enter the Olympics, for example, as the UK, not as England.