By Lefteris Karagiannopoulos

ATHENS (Reuters) - Dimitris, a 31-year-old who delivers souvlaki in Athens, mounts up and rides off into the whizzing traffic of the Greek capital, his battered motorbike one of around a million uninsured vehicles on the streets of Greece.

According to the European Road Safety Observatory, Greeks admit to dangerous driving more than any other Europeans and road fatality levels are the highest on the continent. Numbers of insured drivers are low, however.

Costas Bertsias, spokesman for Auxiliary Fund Insurance of Liability, a guarantee fund for claims on accidents involving uninsured drivers, said 15 percent of vehicles in Greece are uninsured, the highest level in Europe.

"Today the numbers of uninsured vehicles are increasing by the day," he said.

Like many Greeks on low incomes, Dimitris, who declined to give his family name because he was worried about being fined, is being squeezed from every side and cuts down wherever he can.

"Yes I haven't insured my motorbike, how can I? I'm paid only the basic salary and I have to foot my rent bill and feed my son," he says. "And of course I can't just keep the motorbike off the streets. I would lose my job."

An increase in tax on vehicle insurance from 10 to 15 percent passed by parliament last week as part of the latest bailout package agreed by the government in Athens to shore up Greece's tottering finances is unlikely to help.

"This can only be a deterrent to people insuring their vehicles," says Ioannis Votsaridis, chief executive of Interlife Insurance, one of Greece's top insurers, who says the industry is already facing a huge drop in demand after years of recession.

He said Interlife had absorbed the cost of the latest tax increase instead of passing it on to customers and has tried to react by offering a broader range of contracts.

"We have even offered insurance contracts for a few days' duration," he said. "But don't be fooled by our healthy performance, the insurance industry has lost more than 1 billion euros of turnover in the last few years."

According to the most recent figures from industry association Insurance Europe, motor vehicle premiums in Greece dropped by 13.3 percent between 2012 and 2013, by far the sharpest fall of any country in Europe.

As the numbers of uninsured drivers has grown, the burden on other drivers has grown sharply, saddling the insurance system with more debt and adding to the length of time it takes claims to be settled.

"Today, drivers have to wait for at least a year to a year-and-a-half to get their payments," said Bertsias.