Eluned Morgan’s comments come as the Welsh government reviews restrictions imposed in December.
There are “very positive signs” that Wales is “coming to the peak” and “possibly turning the corner” on the coronavirus wave, a minister has said.
Health Minister Eluned Morgan spoke ahead of Friday’s announcement of the latest review of Covid restrictions.
“It would be a huge, huge relief” if Wales was reaching that stage, she said.
Wales’ rules were last tightened on 26 December, meaning no more than 50 people can attend a sporting event.
The rules have forced many teams to have to play behind closed doors.
Social distancing restrictions are also in place in businesses and a rule of six applies in hospitality venues such as pubs and restaurants.
Welsh Tory Senedd leader Andrew RT Davies called for the rule of six and sport restrictions to be scrapped.
He said it was “time to move forward as we learn to live with the virus”.
Giving evidence to the Health and Social Committee on Thursday, Ms Morgan said: “I know that in London about 10% of the population are ill with Covid and in Wales it’s about 6%.
“So that’s a significant difference and, obviously, we’re hoping that we’re coming to the peak now.
“And if we arrive at a peak of 6% and they’re at 10% then, actually, there is real cause to celebrate, that is a snapshot that you can look at.
“We are clearly keeping a very close eye on the data at the moment but there are some very positive signs, I’m pleased to say, in terms of us possibly turning the corner, which would be a huge, huge relief.”
Case rates fall
The Wales case rate has fallen to the lowest level since 27 December – 1,492.4 per 100,000 people over seven days.
While that includes a change in policy where people who are not showing symptoms but test positive on lateral flow devices no longer need PCR tests, cases were falling three days before that happened.
The depth of the fall is also deeper than can just be explained by that change.
Neath Port Talbot has the highest case rate still, with 1,893 cases per 100,000 and there are now 92% of local communities with case rates above 1,000 – the proportion has dropped from the 98% seen last week.
Pembrey & Burry Port and Abercynon are the two highest with 2526.2 cases per 100,000.
The positivity rate has fallen to 44.6% – the lowest since 27 December 2021, with Anglesey having the highest rate at 48.3%.
All age groups are showing a decline in cases, especially those younger age groups, which were driving the spike over the Christmas areas, with all but four local council areas in Wales also showing a drop in case rates among the under 25s.
An average of 8.5% of all primary pupils and 14.3% of all secondary pupils were absent due to a known Covid-reason around 6 January.
Meanwhile, Welsh ministers said they have no plans to cut the self-isolation period for people who test positive for Covid-19.
In England, the self-isolation period is being cut from seven to five full days.
A Welsh government spokesperson said:”We will be guided by the evidence and look forward to seeing the clinical evidence that has informed this decision.”
From Monday, people in England will be able to leave isolation after negative lateral flow tests on days five and six.