Chloe Middleton, from Buckinghamshire, is thought to have been the youngest Briton killed in the pandemic.
An 18-year-old man who died in hospital in Coventry at the weekend having tested positive for Covid-19 was being treated for ‘significant underlying health issues’.
Ms Middleton's family urged the public to heed safety advice and take ‘this seriously’.
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Her mother, Diane Middleton, wrote: ‘To all the people out there that thinks it's just a virus, please think again. Speaking from a personal experience, this so-called virus has taken the life of my 21-year-old daughter.’
In an appeal to take preventative action, Ms Middleton's aunt Emily Mistry described how her niece ‘had no underlying health issues’.
Ms Mistry wrote: ‘My loved ones are going through the most unimaginable pain, we are shattered beyond belief ...
‘The reality of this virus is only just unfolding before our very eyes. Please, please adhere to government guidelines.
‘Do your bit. Protect yourselves and protect others!! The virus isn't spreading, people are spreading the virus.
‘Life as we know it has changed dramatically but unless we all act now to protect ourselves and others, the longer this turmoil and anguish will go on ... ‘
Ms Middleton's sister, Amy Louise Middleton, said her children ‘couldn't have had a more loving, crazy nutcase for an auntie and we wouldn't have had it any other way’.
She wrote: ‘She went above and beyond for me and was my best friend even though she had a habit of pinching my clothes, so many great memories that I'm so, so, so grateful we got to make and share and that will never be forgotten!
‘Her only concern in life was if she looked bloody bloated so please don't take this virus lightly because you never know what's around the corner ... ‘
She added: ‘About time people took this seriously, before too many people end up in this devastating position!’
A total of 422 patients who tested positive for coronavirus had died in the UK as of 1pm on Tuesday, the NHS said.
The country is three days into a three-week lockdown ordered by Prime Minister Boris Johnson in an effort to stem the surge in cases.
Shops, schools, pubs and offices have also been forced to close in an attempt to reduce the spread of the virus and ease pressure on the NHS.