The move, which will be voted upon on 12 July, would end social distancing and the mandatory use of face masks.
It means there could be full stadiums for the start of the Premier League season in August.
However, the PM said some venues may choose to make use of the NHS vaccine passport service should they wish.
Wimbledon has seen an increase of crowds this week, with Centre Court at 75% capacity. The All England Club have confirmed they will increase this to 100% for the quarter-finals, the semis and finals on both Court one and Centre Court.
There will also be hope for full stadiums during England’s Test series against India starting on August 4, as well as at Glorious Goodwood at the end of July.