United broke the PL transfer record with Veron in 2001
http://news.bbc.co.uk/sport2/hi/football/teams/m/man_utd/1423604.stm
and then set a new record with Ferdinand the following year.
http://news.bbc.co.uk/sport2/hi/football/eng_prem/2143600.stm
Abramovich bought Chelsea in 2003 and it took him three years to beat the Veron fee with what he paid for Sheva and another four years to break the league record (for the first time!) with Torres deal. United were spending huge amounts long before Roman's arrival.
And let's not forget, Laporte is supposedly going to be City's record signing, which is still less than the fees paid for Lukaku and Pogba and basically on par with Angel Di Maria's. But it's only the likes of Chelsea and City who are responsible for big transfer fees, obviously.