The first pilot event will be a comedy night in Liverpool, where people will be tested before and after the show.
Manchester City face Tottenham in the Carabao Cup final seven days later with 8,000 fans watching and the month-long scheme will conclude with the FA Cup final on May 15, when 21,000 fans will be attending.
Evidence of vaccination, proof of a negative test, or natural immunity due to having had the virus recently will all be factors in the certification process.
'We are doing everything we can to enable the reopening of our country so people can return to the events, travel and other things they love as safely as possible, and these reviews will play an important role in allowing this to happen'.
More than 40 Conservatives have signed a letter publicly opposing the use of vaccine passports in a campaign which has brought together ex-Conservative and Labour leaders Iain Duncan Smith and Jeremy Corbyn.
Downing Street said the pilot system "could allow higher-risk settings to be opened up more safely and with more participants".
Ministers believe the scheme will be most useful in managing the risks where the are large numbers of people in close proximity such as music festivals, sporting matches and nightclubs.
The UK has given 31 million people a first vaccine dose and a second dose to more than 5 million.
It added that it should not be used for public transport or entry to essential shops.
It will also not apply initially to businesses which are set to reopen over the coming weeks such as pubs, restaurants and non-essential retail.
The state-funded health service is developing digital and non-digital ID, the government said.
"The Carabao Cup is a prized asset of the English Football League (EFL), a great competition for clubs to win and always a fantastic occasion so we are absolutely delighted to see supporters back for the 2021 final, in what will hopefully be another important milestone along the way to a full return of fans", EFL chairman Rick Parry said in a statement.
There will also be tickets offered to local residents in Brent, the area where Wembley Stadium is in London.
The government also confirmed it will grade countries according to a "red, green, amber" traffic-light scheme when outbound worldwide travel reopens on May 17 at the earliest.
There will be no isolation requirement for travel from countries in the new green category, although pre-departure and post-arrival tests will still be needed.
The "red" and "amber" restrictions would remain as they are now - with the requirement to enter quarantine or self-isolation upon return.