Şükür then moved to Italy again, this time to Inter Milan, scoring six goals in 35 official matches. His appearances were limited by the presence of Ronaldo and Christian Vieri in the team's attack and January 2002, after one and a half seasons, he signed with another team in the country, Parma FC, but was unable to produce again, only finding the net three times. Having been released, on 9 December he joined Blackburn Rovers in the Premier League for the remainder of the campaign, signed by former Galatasaray manager Graeme Souness. His spell began with him sustaining a broken leg in training which ruled him out for two months, after which made his debut for the club on 1 March 2003, replacing the injured Egil Østenstad at half time in a 1–0 home win over Manchester City; he scored twice from nine appearances, both goals coming in a 4–0 defeat of Fulham at Loftus Road on 7 April.
Şükür returned to Galatasaray on 7 July 2003, after failing to negotiate a new contract with Blackburn. He scored 12 times in 28 league games in his first season and 18 in the following, with the team winning the 2005 Turkish cup during that timeframe. Also, on 3 December 2003, he found the net twice in a 2–0 home defeat of Juventus F.C. for the 2003–04 UEFA Champions League; in November 2003, to celebrate UEFA's Jubilee, he was selected as Turkey's Golden Player by the Turkish Football Federation, as their most outstanding player of the past 50 years.