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Can someone help me understand how fast Real Bedford could possibly get to the Premier League if they continue winning each league they play in?
They play Spartan South Midlands Football League Premier Division. That's Level 9 in the English league system. So, 8 years is a minimum, even if they win their league each year.
With their budget you could create club in, for example, Latvia, and would possibly get into UEFA European competitions in 3 years, starting from bottom.