Roy Hodgson has questioned Michel Platini's argument that Uefa's revamped "week of football" scheduling in qualification for Euro 2016 will thrust the international game back into the limelight, and instead insisted the new timetable actually benefits only the clubs.

Uefa, which has increased the number of teams at the finals in France from 16 to 24, has also introduced new six-day international windows running from Thursday to Tuesday, with teams asked to play three double-headers over the qualification campaign. That will involve games taking place every night in those periods and Platini, the Uefa president, has admitted the new programme was "a political decision" aimed at thrusting the international game back into the limelight given the strength of the Champions League and domestic competitions.

Yet Hodgson – whose England side have been drawn in Group E with Switzerland, Slovenia, Estonia, Lithuania and San Marino – believes the system will actually deprive national managers of even more time to work with their players. "It won't affect the clubs, but it will affect the national teams," he said. "When I was manager of Switzerland [from 1992-95] we had two weeks in every window. Then it went down to 10 days, then eight or nine, and now it could be six days if you're playing Thursday and Sunday. I don't understand how that can be championed as something to help the national teams: if you want to help the national teams, have more time for preparation.

"As far as the clubs are concerned, they'll be rubbing their hands together because they will get the players back quicker. For the national teams, though, you don't have to be a statistician or a rocket scientist to work out it's getting harder for us. We don't really get the time with the players we would like. We want to work with them and do our bit of tactical work as well, not just the club sides."

The greatest concern for Hodgson was a double-header starting with a Thursday evening fixture, potentially just four days after many of his key players might have been involved in televised Premier League games. "That would mean Monday is a write-off, Tuesday too for the older players because they need a two-day recovery, leaving one day, the day before the game, to prepare the team," he said. As it transpired, the qualifying fixtures have given England only one game on a Thursday night – against San Marino on 9 October this year – though the issue could remain for other national sides whose players feature in league fixtures on Sundays before international matches.

Group E has handed Hodgson a reunion with Switzerland, whom he led to the 1994 World Cup and steered to Euro 96 before leaving to join Internazionale, and a team currently ranked No6 in the world. Indeed, England's first game in the group will arguably be their toughest, in Switzerland on Monday 8 September. "We won't have any fear and we'll go into every game playing to win," said Vladimir Petkovic, who takes over from Ottmar Hitzfeld after the World Cup to oversee the Swiss campaign.

Estonia are under the stewardship of Magnus Pehrsson, who played briefly alongside Chris Waddle for Bradford City in the mid-1990s and has since worked as an expert analyst for Swedish television alongside Hodgson. The Slovenia head coach, Srecko Katanec, admitted relief at having avoided the heavyweights of "a Spain, Holland or Germany", although the new San Marino manager, Pierangelo Manzaroli, said: "England will be the winner of the group."

There is an irony that Scotland and Republic of Ireland, who had originally proposed in 2007 that the European Championship be swollen to 24 teams, were paired against each other in arguably the hardest qualification section.

Group D is completed by Germany, Poland and Georgia, together with Uefa's 54th member, Gibraltar. "It's the toughest group but it's an exciting one," said Martin O'Neill, who is embarking upon his first competitive campaign as the Republic's manager. "The games against Scotland will be great occasions, I hope. It's tough, and there are other groups we might have preferred to be in, but we'll get on with it."

The Scotland manager, Gordon Strachan, who succeeded O'Neill at Celtic in 2005, insisted there was "a chance of straight qualification".

"Every tie has something in it," he said. "You've got Gibraltar, new to the competition; Germany, one of the best teams in the world; then there is the Republic of Ireland and the two sets of supporters will turn those games into a cup tie. It's a terrific, terrific draw."

Wales were paired in Group B with Belgium, an emerging force driven by a brilliant generation of young players, from the second pot of seeds. "We're a bit gutted that they came out but, generally, it's positive and a good draw for us," said the Welsh manager, Chris Coleman. "It will be a tight section and hard for us, but I think we've got a good chance. We've got to nail the first two games [against Andorra and Bosnia-Herzegovina], but the new format gives us a better chance."

Northern Ireland, seeking a first appearance at a major finals since 1986, were drawn with Greece, Hungary, Romania, Finland and the Faroe Islands. "We have teams in there who I believe we can compete with and take points from," said the manager, Michael O'Neill.

The five-team Group I will be made up by the hosts, France, who will play friendly fixtures against the other nations, though the results will have no bearing on qualification.