Joe Anderson said his eldest brother was currently receiving care at the Royal Liverpool University Hospital and is in a “very serious condition”.
“10 mins ago my sister-in-law a Nursing Sister has told me my eldest brother her husband has got Covid-19 he is in the Royal LivHospitals in the ICU in a very serious condition,” he tweeted on Friday evening.
He also highlighted a video shot inside the hospital’s ICUs, featuring a plea from critical care consultant Dr Richard Wenstone for people to stick to the rules, as he warned: “We’re under a lot of pressure every day now. My biggest worry is we’ve not seen the peak of the second surge yet.”
Mr Anderson wrote: “Please watch the video, follow the rules and understand why we all need to fight the enemy Covid.”
Liverpool had the third-highest infection rate in England in the week to 12 October, according to Public Health England figures, with 3,389 cases – which translates to 680 infections per 100,000 residents.
Liverpool, Wirral, St Helens, Sefton, Knowsley and Halton were the only parts of England to initially be moved into the “very high” Covid alert level this week as the government unveiled its new three-tier system.
Earlier on Friday, Mr Anderson – who had previously called for a so-called “circuit-breaker” lockdown – joined Liverpool city region leaders in branding the tier system a “shambles”, after gyms were allowed to remain open in Lancashire as it was also elevated to Tier 3.
It came after gym owner Nicholas Whitcombe was fined £1,000 when he refused to close Body Tech Fitness in Moreton, Wirral, on Wednesday.
Liverpool city region leaders argued that they had been given no choice on the package of measures, while the government claimed the interventions were a result of consultation with local authorities.
“Liverpool City Region has demanded immediate clarification on why Lancashire gyms are allowed to stay open and Liverpool's close,” Mr Anderson had tweeted. “Inconsistent mess, we now have Tier 3 A and Tier 3 B.”
In a joint statement, Liverpool city region mayor Steve Rotheram and leaders of the six boroughs said: "We simply will not accept our region being treated differently to other Tier 3 areas, without robust scientific evidence.
"These inconsistencies in restrictions between areas within the same tier risk undermining the new system from the beginning.
"So today we are once again demanding that government urgently supplies us with the scientific evidence behind their decision to close gyms in our area, while allowing them to stay open in other areas."
"People everywhere need to know and understand what Tier 3 means."
The UK's largest gym chain, Pure Gym, said earlier this week it is considering legal action over the government's decision to close gyms and fitness centres in the Liverpool area.
A government spokesman said: "Soft play and car boot sales, which remain open in Merseyside, are closed in Lancashire, whereas the opposite is the case for gyms. Arcades, betting shops and casinos are closed in both areas.
"Intensive discussions with local leaders in both areas identified those which should close in each.
“We have been clear that additional interventions above the baseline for very high alert areas are subject to consultation with local authorities based on local evidence.”