The news, if implemented, will help hospitality services, including many chains and independents operating in Peterborough, get back to a somewhat normal way of working.
One-way systems, screens and mask-wearing while moving around might remain for hospitality venues but customer numbers will no longer be limited, The Times said.
Audiences in theatres and cinemas will have to wear face coverings during performances, while there will be strict guidance on ventilation and staggered entry, the newspaper reported.
Kate Nicholls, chief executive of trade body UKHospitality, said: "These reports are very welcome if true.
"However, we must wait to see the full detail of plans as any restrictions in venues will continue to impact revenue and business viability.
"A return to unrestricted trading on June 21 is critical and will mean hospitality businesses (can) come off life support and be viable for the first time in almost 16 months.
"We urge the government to confirm reopening dates and these plans at the earliest opportunity, which will boost confidence and allow companies to step up planning and bring staff back."
The next round of lockdown easing will see hospitality venues welcome customers indoors with the rule of six from no earlier than May 17.
Five weeks after that, the rest of lockdown restrictions are expected to ease, with clubs being able to reopen their doors on June 21 for the first time in 15 months.