A UK tech firm is offering video consultations with doctors via mobile phone, in a bid to repeat the success of British startup apps such as Hailo and Just Eat in which a taxi or a meal is a phone-tap away.

With the NHS under growing strain, the Liverpool-based startup, called Dr Now, is targeting its new mobile app at tech-savvy people who do not want to wait for an appointment with a GP, as well as businesses looking to save sickness-related costs.

It has recruited 250 doctors so far, led by Dr Andrew Thornber, one of the startup’s four founders, and picked up 300 active users since its “soft launch” (without marketing) on 22 June. The venture charges £4.99 a month for the subscription health service while a one-off consultation costs £29.

The company guarantees that the medicines and prescriptions needed by patients will be delivered to their door by the next morning – or within four hours for customers in central London.

Dr Now will jostle for patients with two other recent UK startups, Babylon and PushDoctor, which also offer video consultations with qualified doctors and issue prescriptions, referrals or sick notes within hours.

Babylon, which has cut its monthly subscription from £7.99 to £4.99, also sends some diagnostic tests to the home, such as a cholesterol blood test. The startups are following in the footsteps of US services such as Doctor on Demand and MD Live.

Babylon was the first such UK venture and now has more than 100,000 patients. It was launched in April 2014 by former Goldman Sachs banker Ali Parsa, who also set up Circle Health. That healthcare firm controversially pulled out of a contract to run a Cambridgeshire hospital in January – the first privately run hospital in the UK – causing a storm of protest over the use of private firms in the NHS.

Seeking to defuse any criticism over yet another private healthcare startup, Dr Now consultant Savvas Neophytou stresses: “We are not replacing GPs. All we are doing is providing a solution for today’s go-to society.”

The former Panmure Gordon pharmaceuticals analyst, who has a PhD in pharmacology, believes there is enough demand for several players, all of whom aim to plug the gap in primary care caused by an overstretched NHS.

All three UK ventures are registered with the Care Quality Commission, an independent healthcare regulator.

The vast majority (90%) of GP diagnoses do not rely on a physical examination, Neophytou claims, making video consultations possible – and far more convenient than a trip to your local GP practice. If Dr Now’s UK-trained, UK-registered doctors cannot help via virtual consultation, they will refer patients to the NHS.

Recently, Neophytou’s wife, whom he jokingly describes as a luddite, discovered a rash on her foot – just as the couple were planning to visit Center Parcs with their three children for their 11th wedding anniversary. So she downloaded the app, had an instant consultation with a doctor and had the medication delivered at home, in time for their trip.

Neophytou reels off the stats: one in six people wait more than a week to see a GP. That has led to growing numbers of people going to A&E departments – more than 20 million a year – nearly 40% of whom are discharged without any treatment.

“Millions of people who go to A&E just needn’t be there,” he says.

The NHS was pushed to breaking point last winter when record numbers turned up at A&E departments, prompting other hospital operations to be cancelled.

A Citizens Advice report showed that people aged 18-34 are more than twice as likely to go to A&E or an NHS walk-in centre when they cannot see a GP compared with those aged 55 and over.

The survey found one in seven people (14%) aged 18-34 and one in 17 (6%) aged 55 or over were unable to see a GP the last time they tried to make an appointment.

According to the survey, one in eight (13%) of younger adults did not get any professional help for a health problem when they were unable to see their GP.

The British Medical Association says: “New technologies have great potential to enable the public to manage their health more effectively and lessen some of the unprecedented pressure the NHS is facing from rising patient demand, falling resources and staff shortages.

“However, remote or recorded consultations with an attached fee have their limitations. Many members of the public will be unable to afford this service and all patients who have serious concerns about their health should physically go and see their doctor. This will always be the best way of assessing someone’s health needs.”

The founders of Dr Now, who have ploughed about £800,000 of their own money into the startup, are so confident of its success that they are already talking to potential partners abroad to roll out the service in places such as Dubai and Abu Dhabi. They also have their eyes on Ireland, China, India and north Africa – targeting countries with large growing middle classes.

While catering for individuals who are frustrated with the NHS, even richer pickings can be had from pitching the service to businesses – persuading them to provide subscriptions as perks to employees so they do not have to take time off work to attend GP appointments.

The Dr Now website, which boasts it is the world’s first website to diagnose and deliver medicine, even has a corporate page that lets businesses calculate potential cost savings, based on the number of staff and average salary. It is in discussions with several big pharmaceutical companies.

Dr Now’s full launch comes in October, “when the nights are drawing in and people are getting coughs and colds”, says Neophytou.

• This article was amended on 1 July to correct Savvas Neophytou’s job title