Mr Johnson had postponed the changes, which were meant to come in on August 1, amid concerns over a second wave of coronavirus.
At the time, Professor Chris Whitty, the chief medical officer, said the country had “probably reached near the limit, or the limits” of what can be done to reopen society.
Wedding receptions of up to 30 people will be allowed from Saturday, as will the reopening of casinos, bowling alleys and skating rinks. Beauty salons, tattoo studios and spas will be able to offer all “close services and treatments”.
All staff offering close contact services, including hairdressers, will now be required to wear a surgical face mask in addition to a visor, following concerns that visors did not offer enough protection.
On Thursday, Mr Johnson said he “will not hesitate to put on the brakes if required, or to continue to implement local measures to help to control the spread of the virus”.
He added: “At every stage, I have said our plan to reopen society and the economy is conditional and that it relies on continued progress against the virus.”
Plans to start indoor performances with socially-distanced audiences and pilots of larger gatherings in sports venues and conference centres will also resume.
This weekend’s final of the World Snooker Championship in Sheffield will be the first pilot event. Allowing spectators at sporting events is planned for October 1.
Pilots at the Goodwood races, the World Snooker and county cricket games earlier this month were suspended when Mr Johnson put the brakes on easing lockdown measures after concerns over a second wave.
In addition, indoor play and soft play centres will reopen, provided they introduce coronavirus-secure measures.
Commenting on the new tougher fines, Priti Patel, the Home Secretary, said: “I will not stand by and see these sacrifices undermined by a small minority of senseless individuals.
“These measures send a clear message – if you don’t co-operate with the police and if you put our health at risk, action will follow.”
Mr Johnson said: “We must remain focused and we cannot be complacent. That is why we are strengthening the enforcement powers available to use against those who repeatedly flout the rules.”