The ones most likely to lead to a reaction are 'permanent' chemicals used to colour hair brown or black for up to six weeks.
One medium-brown dye in Clairol's Nice '* Easy range contains six such compounds, The Mail on Sunday has found. Allergic reactions to these chemicals can include burning sensations, an itchy scalp, flaking skin and rashes. In rare cases they can cause the face to swell up, hair loss and breathing problems.
Since November 2011, manufacturers have had to place warnings on the side of hair dye packs under European Union regulations. These say that each time a person dyes their hair, they should carry out an allergy patch test beforehand.
But Dr White believes the warnings are not prominent enough.
'The new warning is on the side,' he told The Mail on Sunday. 'It doesn't hit you in the face like a cigarette warning does. We need to make the warnings explicit. Consumers are not as effectively protected as they should be.'
The hair dye industry is worth millions of pounds in the UK, with dyes used 100?million times a year in homes and salons.
Yet the European Commission estimates that between one in 50 and one in 100 people who use hair dyes suffer from an allergic reaction to them at some point.
An investigation by this newspaper found Clairol's Nice '* Easy Natural Medium Brown dye contains six of the chemicals on the SCCS list of those that might not be safe.
L'Oreal Excellence Crème Natural Mahogany Brown contains three, while its Garnier Nutrisse Crème Dark Golden Brown product includes two.
In 2011, Julie McCabe, 38, a mother of two from Keighley, West Yorkshire, was taken to hospital suffering from breathing problems that started while she was dying her hair using L'Oreal's Preference. She suffered heart failure and brain damage, and spent a year in a coma before dying last November.
The previous month, 17-year-old Tabatha McCourt, from Airdrie in Lanarkshire, started vomiting and collapsed after colouring her hair. She later died in hospital.
In neither case was it proven that chemicals in the dyes were to blame. However, personal injury lawyers say they are hearing from far more consumers on the issue.
One lawyer, who did not wish to be named, said there had been a 'massive increase' in the number of cases lately.
The Cosmetic, Toiletry and Perfumery Association, which represents hair dye manufacturers, said all dyes underwent extensive safety tests to prove they are not toxic or carcinogenic and that the existing warnings were sufficient.
A Clairol spokesman said millions of people used hair dyes 'without experiencing any adverse effects', although she acknowledged reactions could occur 'for a very small number'.
A L'Oreal spokesman said: 'We are confident the warnings and advice on our product packs are sufficient to inform people of the risks and they clearly state the importance of carrying out an allergy test 48 hours before using the colorant.'
An EC spokesman said it was not the job of their scientific advisers to dictate how best to protect consumers.
He said: 'In general, hair dyes are safe. Only in rare cases can they cause allergic reactions. To determine an exact spot where the warnings should be placed seems disproportionate for a cosmetic product.'
- Mail On Sunday