Culture, Media and Sport Secretary Jeremy Hunt said he was "thrilled" about England's victory and hoped they will continue to improve in a "quiet, British way".
After a speech at London's Victoria and Albert Museum, Mr Hunt said: "I watched bits of it (England's 1-0 victory over Ukraine). Obviously I'm absolutely thrilled and keeping fingers firmly crossed.
"England seems to do best when we don't have the highest expectations so I think it's best not to ramp up expectations too much. Hopefully we'll continue to go from strength to strength in a sort of quiet, British way."
Mark Perryman, a member of the LondonEnglandFans supporters group, talks about the unexpected success of England at Euro 2012.
Steven Gerrard is proving to be one of the players of the tournament at Euro 2012.
England have qualified for the Euro 2012 quarter-finals after a 1-0 win over Ukraine and will now face Italy on Sunday.