A certified aeroplane, registered in the UK, is statistically likely to have a fatal accident every 70,000 flying hours.
A reasonally usy PPL, flying about 35 hours per year, has therefore about a 1 in 2,000 chance of being in a fatal accident, in any one year.
Around 2,500 people die in car accidents on British roads annually. Assuming we all travel by car at some point, and there are about 60 million of us: any one of us has about a 1 in 24,000 chance of being killed in a road accident in any given year.
So no, flying light aircraft is not as safe as driving.
On the other hand, according to
Oxford University the average Brit has a 1 in 396 chance of dying from cancer in any one year.
So, in 2012, an average PPL has a 1 in 2000 chance of dying flying, a 1 in 24,000 chance of dying driving, and a 1 in 400 chance of dying of cancer (and, incidentally about the same odds of dying of heart disease, or about 1 in 4,000 chance of dying of dimentia).
So, if you are too young to worry about dimensia yet, and fly about 35 hours per year, in 2012 your odds are:
1:400 dying of cancer
1:400 dying of heart disease [although that's for the whole population, so hopefully holding flying medicals the odds are better for us.]
1:2,000 being in a fatal air accident (although you might not be the one to die)
1:24,000 dying in a road accident
So the throwaway comment about driving risks is not fair. But, you are far more likely to die of cancer than you are flying. On net, I'd also much rather die flying (although even more so, I'd rather not die).
If you fly a lot of hours, at about 175 hours per year, you about break even on flying and cancer.
(Airline flying is a totally different beast of course - their fatal accident rate is so tiny that it's insignificant, and getting better. But they are regulated, trained and tested to an extent that would abolish GA.)
G