Speaking to councillors at a full council meeting, Mayor Jones paid tribute to NHS workers who are doing a ‘sterling job’ on the front line.
But Mayor Jones also warned people to continue to stick to the rules and said the Government could reimplement the tier system as a way to tackle hotspot areas.
A new four-step plan to reduce the lockdown could result in all legal limits on social contact lifted by June 21, if conditions are met.
Shops, hairdressers, gyms and outdoor eating and drinking could reopen on 12 April 12 in England under plans set out by the Prime Minister Boris Johnson.
From May 17, two households might be allowed to mix in homes, while the rule of six could apply in places like pubs.
It requires four tests on vaccines, infection rates and new coronavirus variants to be met at each stage.
Mayor Jones said: “I cannot stress enough the potential for these dates to slip by a number of weeks if we see a considerable rise in infection rates and hospitalisations.
“Government has said that this will be the last lockdown but the possibility of regional or localised restrictions is not off the table.”