Sarah Brisdion, whose son Hadley, five, has cerebral palsy, cannot use baby changing facilities as he is too heavy.
Mrs Brisdion, from Hampshire, says the experience "brings tears to my eyes".
Government regulations do not make providing such facilities a legal requirement and, according to charity Changing Places, there are only 750 appropriate toilets in the UK.
The charity, which has developed ideal facilities, estimates there are 250,000 people across the UK with disabilities that mean they are in a similar position to Hadley.
Mrs Brisdion, from Brockenhurst, says the nearest suitable changing area she can use is in West Quay shopping centre in Southampton, nearly 15 miles away.
A video showing Mrs Brisdion's campaign has been viewed thousands of times on social media site Facebook.
Mike Le-Surf, of Changing Places, said the problem was stopping many people from leaving their house, because changing someone on a "dirty floor" was "not acceptable".
In 2013, the government reviewed building regulations, but did not make it a legal requirement for new large developments to include adult changing tables, although it said providing such facilities was "desirable".
A Department for Communities and Local Government spokesman said a further review was being carried out to see if changes to building regulations are necessary.
A full Changing Places bathroom takes up 12m sq (130 ft sq), and costs Â£18,000, but campaigners say simply putting a static changing bench into wheelchair-accessible toilets would make a huge difference to many carers and people with disabilities.
Mrs Brisdion said she was planning to contact Southampton Football Club, Southampton's train station and Southampton General Hospital about her campaign.
University Hospital Southampton NHS Foundation Trust said changing room toilet facilities were already under construction at Southampton General Hospital, while Southampton FC said installing a changing room was "on the table for discussion".
The station is yet to comment.
A woman who faces putting her disabled son on public toilet floors to change him is demanding better facilities.