The only way it could work would be to abolish England entirely and break it up into regions.
The issues Scotland has are felt throughout the UK, and Scotland therefore has a lot in common as far as wanting powers as do regions of England out with the immediate surroundings of London. This in essence is why this result could be better for the regions of England.
Part of the problem is that London is a bit in the same situation as the old "every road leads to Rome" saying, and amongst many types of businesses in London, anything but Zone 1 or maybe zone 2 is never even considered when deciding where to set up offices as a result.
So even a lot of London suburbs remain underdeveloped and ignored compared to what their population size would justify because we have the behemoth next door sucking everything in.
With the new-ish London rail projects that are increasingly aimed at cutting through central London, as well as the new orbital overground projects (one completed, another one further out in planning stages AFAIK) there'd be lots of opportunities to break the stranglehold of central London by making more of the smaller centres at the edges of London more attractive by making them more accessible.
I hope we'll see more projects like that - making bypassing (central) London easier both on a local level but also nationally.
I think that will actually have far greater long term impact on the UK than devolving more powers to regions (though I'm all for that as well).
The problem is that fixing this would be a long game: To get maximal effect you'd need to upgrade many routes to handle more frequent, faster trains, and increase train frequencies on many of those routes at potentially significant short term losses and commit to continue running them for a decade or more before there'd be much chance in changing peoples decisions about where to place their companies and where to live and work.
David Cameron's goal from this referendum was to win and close down any suggestion of real reform. There's significant danger that just a few weeks of chatter about it remain.
Growing up, I had absolutely no problems comprehending that my county (cumbria) was part of a region (the north-west), which is why we got Manchester's news on the TV. That region was then part of a country, and a few countries made up our nation.
We already have these tiers of identity. We already have borough seats, county seats, city seats, etc. If we federalized the UK along the same sort of regional identities the BBC does, I don't believe we'd suddenly lose any county/country/national identity.
(Perhaps not exactly the same boundaries, but I can't help looking at their map and thinking - yeah, that's a good start)
It's less of a problem for the Germans because they are comparatively more invested in europe, for example using the currency.
If you want to keep sending an England team, keep sending an England team. Big deal.
As I noted in a different comment: The current situation of an England team is an historical oddity: England, Scotland and Wales are considered constituent countries of the UK. Only a handful of countries worldwide have constituent countries, and the exact details of in what context they are treated as countries vary greatly.
But if the UK was turned federal, there's no reason why the new federal entities would be considered countries any more than e.g. the states of Germany are, even though in the case of the states of Germany, many of the states still closely match countries with a long history as independent states.
Historically, Germany is quite different to the UK for obvious reasons. I also suspect Scotland , Wales etc would be more likely to table flip when dealing with a UK parliament than say Saxony would.
The EU also works quite well for small nations.
[for those interested, the weighting is done by assigning 1 point per person in a region, and 1.8 points per square kilometer of area and using that to redistribute the seats in parliament across the regions, and is adjusted every 8 years; the 1.8 is/was tweaked to fit political realities at the time - I don't think there's any deeper thinking behind that specific factor]
Norway's electoral system, based on proportionality first, has a very good reputation. Indeed, it scores highest (9.93/10) in the Democracy Index 2012 compared to UK in 16th (8.21/10) and USA in 21st (8.11/10)
Actually, I'd say the bigger problem is that with no attempt towards proportionality, very many people end up with only their last choice of representation in at least some bodies of government -- that is, they are represented, in at least one body of government and possibly at all levels of government, exclusively by people who they view (and who view them) as enemies.
I think you'd find that on the contrary a lot of EU states are terrified of any steps that would legitimise more demands for devolution because they have their own independence movements to deal with.
And if anything, if the UK vote in important EU organs were split, it'd greatly increase UK influence on many matters in all the situations where interests are aligned, because most EU organs does not have representation proportional to population size, and many have requirements for super-majorities or even unanimous decisions on many things. That too would make many of the other large EU countries push back against any attempts to bypass a federal government.