So if I understand you correctly you want to keep the clubs and national leagues as they are and just have a Team GB to replace the four national teams?
In that case I think you would need to re-activate Great Britain as a nation and
1) Change the nationality of all players from those four nations to GBR so they can only be selected internationally for GBR.
2) Set the number of A level caps for all British players to 0, otherwise all currently capped players will be unavailable for Team GB.
2) Give all clubs in those four nations GBR as their "based nation" - like Swansea and Cardiff have ENG as their "nation" but WAL as their "based nation". That should ensure that (most of) the newgens get the GBR nationality.
Now, if you de-activate the four Home Nations at the same time, you would most likely get massive problems with continental club competitions and EURO/WC qualifiers because it would screw up UEFA coefficients and continental qualification for the clubs.
I'm not entirely sure how best to solve this, but a suggestion would be to change the reputation of all four Home Nations to 1. If there are no players with that nationality, their national teams should just consist of grey players and play no role in EURO/WC qualifying. But since the nations still exist and have the same UEFA coefficients, the clubs should still have access to Europe.