The Terrence Higgins Trust wants pharmacies to stock the kits, which have been available online for more than a year.
Currently, it is estimated that only approximately 56 per cent of people who have HIV globally are aware of their status.
In the UK, around 25,000 people remain unaware they have HIV and are unknowingly responsible for the majority of onward transmission.
Additionally, almost half of newly diagnosed cases are diagnosed later than treatment should have started, adversely impacting health and life expectancy.
Early diagnosis can extend the lifespan of sufferers and ensure they do not unwittingly pass it on.
But high street stores such as Boots, Superdrug and Lloyds Pharmacies do not stock the self-test kits.
Dr Michael Brady, Medical Director of Terrence Higgins Trust, said: "It's important to offer a wide range of HIV testing options. We can't rely on everyone going to a clinic.
"Unlike postal testing, with self-testing you do not need to send your sample away and have a stressful wait for the result - you will find out your HIV status privately, in your own space, in your own time, on your terms, within minutes.
"We recently conducted two pilots where we gave away 7,000 self-test kits to people at risk of HIV.
"We found them to be a really popular choice and got very positive feedback.
"Self-testing can empower people who might not have time to go into a clinic or to wait for a result, or who may be put off by stigma around HIV, to find out their HIV status.
"One in seven people living with HIV are not aware they have it. It's never a good idea to be unsure of your HIV status.
"Testing puts you in control and, thanks to treatment, could stop you from getting seriously ill, enable you to live a healthy normal lifespan and prevent you from passing the virus on to anyone else.
"That's why it's so important that we embrace new ways to normalise HIV testing and to make it more accessible.
"Self-testing for HIV has proven to be acceptable and convenient but is still not widely available in the UK; either on the NHS or in the high street for people to buy for themselves like a pregnancy test.
‘Convenient and confidential’
"Wider availability of HIV self-tests would ensure even more people have access to a convenient and confidential means of testing for HIV, help us to increase and normalise HIV testing and ensure more people are aware of their HIV status. "
The only home-testing kit, BioSure, were launched in 2015 but are not available in the high street, only online.
They have just launched into South Africa, where they are stocked by Dis-Chem, the country's second largest pharmacy chain.
In South Africa, seven million people are living with HIV, and nearly 2.8 million are unaware they have the virus.
BioSure founder and CEO Brigitte (corr) Bard said: "While UK retail stores lag behind, South African retailers are stocking it.
"Perhaps it's the 'HIV' in HIV self testing that is the retailer's real barrier?
"Self testing allows people to take responsibility and ownership for their HIV status.
"We wouldn't dream of telling people with whom, how or when they choose to have sex and yet, until now, they have been separated from knowing their own status by a healthcare professional.
"We passionately believe that self-testing can help to reduce HIV infection rates."
The tests use a finger prick blood test to diagnose the virus in just minutes, but are currently only available online.
Boots do not stock the kits either online or in store.
A Boots UK spokesperson said: "We currently do not sell any HIV testing kits, but we regularly review our offer to ensure that we are meeting the needs of our customers.
"We advise anyone with concerns to talk to their GP or local pharmacist."
LloydsPharmacy have the kits available for click and collect, and said due to high demand, they are looking to roll them out in store.
Superdrug did not respond to a request for comment.