The EU, which has the power to set import duties for all member states, intends to impose a 10 per cent import tax on the scooters, despite the fact that equipment for disabled people is exempt from tax.
Charities for the disabled say that the extra cost of buying scooters will have an immediate impact on the number they can afford, meaning thousands of people each year could be denied a vital means of independence.
Professor Hawking, who suffers from motor neurone disease, said: "For many of us with disabilities, a mobility scooter is literally a life line - without it we are locked out further from the world around us. To tax the most disadvantaged in society in this way is simply disgraceful."
Ever since the scooters were first invented 30 years ago they have been classed as equipment for the disabled, making them exempt from tax.
But a little-known body called the World Customs Organisation, which advises governments on import duties, recently issued a document recommending that they should be taxed, as it said they could be used by people without disabilities.
Although many countries, including the US, rejected the advice out of hand, the EU decided to accept it, and has put the scooters in the same tax classification as Formula 1 cars.
The EU's customs code committee intends to enshrine the change in law when it meets later this week.
In the meantime, the tax is already being imposed on charities which buy 25,000 of the scooters for disabled people each year, amounting to a total annual tax bill of 6 million.
Jim Dooley, chairman of the Mobility Bureau, the UK's largest supplier of the scooters through charitable organisations, said: "To say these scooters are not just for disabled people is ridiculous. They have more than 20 features which are specifically designed for disabled people. Does the EU really think fit and healthy people go out and buy these as a lifestyle choice?
"When the EU committee was given a demonstration of this equipment, not one person on the committee had a medical qualification and none of them asked for a formal medical opinion.
"This is a real slap in the face for the disabled. We have tried to get the UK government to fight our corner, but so far they've done nothing."
Peter Gower, 57, a Falklands War veteran who broke his back in an accident while he was posted in Germany with the Royal Army Ordnance Corps, said his mobility scooter - bought for him by a charity earlier this year - transformed his life after he had become virtually housebound.
"Before I had this scooter, I couldn't really get out of the house and had to rely on my wife all the time," he said.
"It was a very difficult, depressing and isolating time. Why anyone would want to put a tax on mobility scooters is beyond me - I mean, no-one chooses to have these things. They're a necessity, certainly not a luxury."
Bryan Clover, a director at the grant-giving charity Elizabeth Finn Care, said: "With the average scooter costing 2,500, and many disabled people already living in poverty, a 10 per cent tax might not seem much for the MEPs but, for many, every penny counts."
Many of the scooters are used by military veterans, and Sue Freeth, director of welfare at the Royal British Legion, described the import duty as "inexplicable".
She said: "This is a tax on the disabled and on the charities who try to make improvements to their lives.
"We are stretched already in meeting the needs of our beneficiaries and this EU tax only makes our job more difficult."
Godfrey Bloom, the Ukip MEP for Yorkshire and the Humber, has written the the Chancellor, Alistair Darling, urging him to vote against the tax change and seek support from other member states.
He said: "Quite why HM Revenue and Customs feels the need to discriminate against disabled people and the charities who support them is beyond me."