Going beyond just the UK, its an interesting problem with a lot of different aspects.
Looking at the tactical aspect, I don't think its that key. But it really depends on exaclty what you're talking about. Tactics were obviously absolutely key in the rise of Hungary and The Netherlands. So if you are taking about a great national team coming from a small nation and manages to revolutionize the sport to some degree, then yes. But if you are simply talking about a great generation of players coming from a smaller nation, then I don't think its really required. Denmark in 1992, Yugoslavia from the same period, and then subsequently Croatia all fit that. They had some top class players who managed to succeed at the biggest of clubs combined with solid talent throughout.
Beyond that, the commercialization of the sport is a big part. The biggest clubs can afford to buy anyone and they pay big wages, even to young players. So those young players are tempted by the fame and fortune. Who can balme them? But is it the best move? Moving to another nation means the player has to adapt and settle to a new culture, perhaps a new language. In many cases, they aren't going to playing regularly for the main squad. Look at someone like Romelu Lukaku - is he going to develop more playing for Chelsea's reserves than he would playing competitively for Anderlecht? There is no one right answer - Fabregas certainly benefitted from moving to Arsenal, and without that loss, Barcelona may not have given Messi the chance they did. But players like Fran Merida and Carlos Vela haven't really benefitted the same way. Samuel Eto'o obviously was better off moving to Spain than staying in Cameroon but every situation is a bit different.
Young players need to play. They develop more playing competitively than against kids. So while first class facilities and coaching is an obvious benefit of a big club, the reduced chances of playing for the first team offset it. So many big clubs can't and won't take a chance. For a club in the top third of the table, using kids costing them points could mean the difference between European football next season or not. One can look at Arsenal stringently sticking to the policy over the past seasons and what is has arguably cost them.
I recently re-read a book I've had for a couple of years, a sort-of journal from a UK football correspondent travelling in Eastern Europe. It goes through the current situation in nations like Russia, The Ukraine, and Croatia, but also the likes of Lithuania, Slovakia, and so on. Hungary is actually one of the nations covered. Lack of developed is a big issue. Most clubs don't have the money to set up proper developmental structures and assistance from the given governments is limited, as they don't typically have the money either. FIFA and UEFA provide some such funding, yet the degree of corruption in the national FAs make it questionable how much of that is put to its intended uses. Youth are given a chance to a degree, but clubs in smaller nations are just as dependent on results as ones in bigger leagues. Qualifying for the CL can be a huge for a given club and most small leagues only get one spot. A lot of small-nation clubs tend to change managers a lot, so there is pressure for immediate results - why take the time to give the kids a chance when one or two losses will cost you your job?
There is also an element of luck involved, especially when it comes to the smaller developed nations. Nations like Belgium, Switzerland, and Croatia are all in a position where they could take that "next step" sometime in the near future, as they have a combination of some established top talent and some quality young prospects. But you need even more than just a quality top XI, because the qualifying processing is so long now and injuries happen. And that's where I think smaller nations will often fall short - they might have quality at the very top but if it drops off below that, they're in trouble.