How did you get to that estimate? Currently both Bundesliga and Serie A are above Premier League, with La Liga only slightly behind. Only two leagues will get an extra spot.
Look at the odds on the three European competitions.
To break it down,
Champions League
English clubs are first and fourth favourites (City, Arsenal)
German clubs are second, ninth and eleventh favourites (Bayern, Dortmund, Leipzig)
Spanish clubs are third, seventh, eighth and twelfth favourites (Madrid, Barca, Atletico, Sociedad)
Italian clubs are sixth, tenth and fifteenth favourites (Inter, Napoli, Lazio)
Europa League
English clubs are first and fourth and fifth favourites (Liverpool, Brighton, West Ham)
German clubs are second and sixteenth favourites (Leverkusen, Freiburg)
Spanish clubs are tenth favourites (Villarreal)
Italian clubs are third, sixth, seventh favourites (AC Milan, Roma, Atalanta)
Conference League
English clubs are first favourites (Villa)
German clubs are third favourites (E Frankfurt)
Spanish clubs are fourth favourites (Betis)
Italian clubs are second favourites (Fiorentina)
English and Spanish clubs have all qualified for the last sixteen, whereas Germany (Frankfurt and Freiburg) and Italy (Roma and Milan) still have to navigate tricky last 32 knockout games.
Also in the Champions League four of the ties are between Spanish, Italian or German clubs, so a big chunk of these clubs will definitely be going out.
I'd be very surprised if England didn't comfortably wrap up one of the extra two spaces.