Culture Secretary Oliver Dowden said he is "hopeful and optimistic" that large-scale crowds will be able to return to sporting events this summer on the day the first restrictions were lifted.
Monday marked the return of grassroots outdoor sport after nearly three months of lockdown, with further relaxations pencilled in for April 12, May 17 and June 21.
From May 17, stadiums could be permitted to host as many as 10,000 fans, while from June 21 the current plan is for restrictions to be lifted completely.
Pilot events will explore how spectators can return safely in large numbers to stadiums.
The rescheduled Euro 2020, which is due to be played across the continent including at Wembley and the Millennium Stadium, straddles June 21.
Dowden, Secretary of State for Digital, Culture, Media and Sport, told Sky Sports News: "For the later matches in the tournament, we'll be looking at substantially more than that (10,000), but that is subject to finding a safe way of doing that.
"I'm very hopeful and optimistic that we will get many, many more people in for the later stage games."
Sports facilities such as football and cricket pitches, tennis and basketball courts, outdoor swimming pools and golf courses were among those reopening on Monday.
Some golf courses opened at a minute past midnight, allowing the action to resume immediately under the cover of darkness.
Neon golf balls were used at the Morley Hayes Golf course in Ilkeston, meaning players were able to tee off seconds after the ban was lifted.
Dowden said on Sky Sports News: "I'm absolutely delighted. After this dreadful long winter of Covid, spring is in the air and grassroots sport is returning.
"We said when we went into these dreadful restrictions that grassroots sport should be the last in and the first out. Today we're delivering on that and it's so essential to everyone's sense of health and wellbeing."
The implementation of the roadmap will depend on targets being met in terms of the prevalence of coronavirus and further delays are possible.
Dowden added: "This is why it's important people abide by the rules as we go through each stage of this. The reason why we've been able to do what we're seeing today is because people have by and large stuck to the rules so far. It's important that at each stage people stick to the rules."
Parents and guardians are being urged to help their children follow the guidance of the Chief Medical Officer Professor Chris Whitty and aim for at least 60 minutes of physical activity a day, with adults advised to take at least 150 minutes a week.
World Cup-winning England cricket captain Eoin Morgan is backing a campaign to get people back playing sport.
He said: "I know how lucky I've been as a sportsperson to play cricket for a living, and to have been able to continue to do so during the ongoing pandemic while so many others have been unable to.
"The reason I started playing cricket as a child was because I loved it, but it also helped me keep fit and active, spend time with my friends, make new ones and have fun.
"I know that so many people, and especially children, have missed out on those vitally important things because of the pandemic so I'm delighted to endorse the #returntoplay campaign.
"With summer - and the cricket season - just around the corner, there's no better time for everyone, young and old, to get back to having fun by getting outdoors, being active and playing sport."
Youth sport is a top priority in the roadmap and last week the Government announced £100million has now been allocated to 266 local authorities across England to support the recovery of publicly-owned leisure centres and gyms.
Grassroots sports and the physical activity sector are also benefiting from £270m in emergency funding delivered by Sport England.
"Over the past year we have prioritised the importance of physical activity, permitting basic exercise at all times," said Sports Minister Nigel Huddleston.
"However the reality is that activity levels have still dropped in lockdown. That's why outdoor grassroots sport reopening today is so important."
British number one Johanna Konta hopes tennis can be one of the sports to benefit.
"I'm so happy people in England are now able to get back on court and enjoy the mental and physical health benefits of tennis," she said.
"It's a great sport for anyone looking to get active outdoors after lockdown at a safe, social distance, and I'd encourage everyone to pick up a racket, no matter whether they're a seasoned player or trying tennis for the first time."