Income tax isn't going to solve this, and I think it's unfortunate Europe tends to very myopically focus on income differences. Progressive income tax does little other than to widen the gap between wage slaves and the rich.
The wealthiest don't have an absurdly high income, they own enough assets to live off dividends and wealth appreciation, which typically gets taxed 20-30%. If they even have an income to be taxed, it's basically symbolic.
This is where the real inequality exists, and it's unfortunately not part of the discussion at all. Instead wagies with slightly higher than average income get portrayed as 18th century mustache twisting top-hat capitalist factory owners.