England are the only European country to have won the World Cup but never be crowned European champions and following a spate of injuries, there are very few indicators suggesting that England's disappointing European record will improve this month.
Whether Hodgson, 64, named on May 1 as England's new permanent manager following the departure of Fabio Capello in February, can bring success remains one of the many unanswered questions facing the Three Lions this month.
In eight finals appearances since 1968 they have only reached the semi-finals twice: in 1968, when only four teams took part in Italy and in 1996 when they hosted the tournament.
Typically for England though, the build-up has been blighted by injuries, with Frank Lampard, Gareth Barry and Gary Cahill all sidelined while Rio Ferdinand was ignored as Cahill's replacement by Hodgson, who preferred Liverpool youngster Martin Kelly instead, provoking the first real row of his reign.
The responsibility for leading England to success passed to Hodgson only weeks before their Group D campaign kicked off against France in Donetsk, Ukraine, on June 11.
Further games against Sweden in Kiev on June 15 and co-hosts Ukraine in Donetsk on June 19 are also considerable obstacles for England to overcome.
One note for optimism perhaps is that England looked organised at the back in Hodgson's first two friendlies in charge which both ended in 1-0 wins against Norway and Belgium. They may not have been pretty displays, but England looked hard to break down at least.
The immediate target for Hodgson is to ensure there is no repeat of England's dismal performances at the 2010 World Cup finals where they went out to Germany in the last 16 after suffering their worst ever World Cup defeat - a 4-1 thrashing.
Capello was widely criticised for those performances and many felt he should have gone immediately afterwards.
However, he stayed on and England regained their self-respect as they cruised unbeaten through the Euro 2012 qualifiers for these finals, winning five and drawing three of their eight games.
The only real blemish in the campaign came 17 minutes from the end of the last one against Montenegro in Podgorica on October 7 when, with their place all but secured, striker Wayne Rooney was sent off for a senseless kick at defender Miodrag Dzudovic.
That ultimately resulted in Rooney, a player with undoubted match-winning pedigree, being banned for the first two matches of the finals against France and Sweden.
The Manchester United striker, who scored more than 30 goals for club and country during the season that has just ended, will be eligible to join the fray on June 19 when England play Ukraine, which could well be their last game in the competition.
There is no doubt that England's players, used to playing at the highest level week in, week out in the Premier League with some of the world's biggest names, have the capacity to do well.
Hodgson at least, who spent 15 months at West Bromwich Albion, does have previous international experience having coached the Switzerland, Finland and United Arab Emirates national sides in the past.
Tournament football at this level is not new to him either, having led Switzerland to the 1994 World Cup finals in the United States - their first appearance for 28 years.
Hodgson had two immediate dilemmas to solve when he took over - the relationship between John Terry and Rio Ferdinand and the captaincy issue.
Capello resigned after challenging the FA's decision to strip Terry of the captaincy because of his upcoming court case in which he will plead not guilty to racially abusing Ferdinand's younger brother Anton of Queens Park Rangers when Chelsea played QPR last October.
Hodgson announced he was leaving Ferdinand out of the squad for "footballing reasons" but just as that dilemma seemed to be over it was re-ignited this week after Hodgson ignored Ferdinand again when Cahill was ruled out.
Losing Lampard, Barry and Cahill to injuries has not helped the cause either and he now has to pep up a midfield which often looks one-paced and one-dimensional.
He has named Steven Gerrard as captain too and if Gerrard can reproduce his old club form in midfield, England could pose some problems for their opponents.
His striker options are also limited because of Rooney's two-match ban and a serious injury to Darren Bent that has ruled him out of the tournament.
So he has put his faith in Liverpool's expensive striker Andy Carroll, who had a good end to an otherwise forgettable season, while Danny Welbeck took his first goal for England well against Belgium but is likely to start on the bench.
Hodgson now faces the hardest job of his long managerial career but leading England to the quarter-finals at least - where they usually go out on penalties - might be a step too far after just a few weeks in the job.