The England team are made up of the best English players (Scotland/Wales have separate teams)
Most of them do play for the bigger Premier League Clubs
Jesse Lingard and Marcus Rashford (Man U)
Eric Dier, Harry Kane, Dele Alli, (Tottenham)
Kyle Walker, John Stones, Sterling (Man City)
Jordan Pickford, goalkeeper - Everton
But I wouldn't say they are the top players at those team clubs. Unfortunately the Premier League is full of foreign players who are outplaying English players.
All the teams that play in England (in the Premier League, Championship, League 1, League 2 etc) have many different competitions where they all play against each other in a knockout challenge and can win the FA Cup, FA Trophy etc.
The top English teams can also compete in various European cups, where they play against the top teams from European countries like Spain (Barcelona, Real Madrid), Germany (Borissia Dortmund), France (PSG) etc and can win the UEFA Champions League and UEFA Europa League.
The English national team can play in the World Cup and the Euros.