When it comes to keeping children safe on the internet, most parents now know what they have to do, says a survey.
One in five children regularly use chatrooms
Some 93% know how to help children surf safely, with 92% saying access is best supervised, says a BT Yahoo/NOP poll.
"It's clear that the many initiatives about the importance of safety on the web are having a positive effect," said BT's Duncan Ingram.
But charity net safety advisor John Carr said it still meant 7% were not getting the safety message.
Battle not over
Most of those polled said banning children from using the net was not the right way to keep them safe, but knowing what steps to take to go online responsibly was best.
"Parents clearly feel more confident about the safety measures available and the practical steps that they can take to keep their children safe on the web," said Mr Ingram, BT Yahoo!'s managing director.
But Mr Carr told BBC News Online that, although the figures were very encouraging, it still meant thousands of children were not being taught the safe surfing message.
"One of the things about the net is that the number of people using it is so huge, so even a small percentage is significant," he said.
When the total number of children in different age groups is taken into consideration - a million nine year olds for example - that seven percent could account for several thousand children, he said.
"So 93% sounds like a wonderful number and is definite progress, but there can be no question of resting on our laurels as we need to get closer to 100%."
Mr Ingram said the figures were not a signal to become complacent, and that the battle to raise net safety awareness was not over.
"Ultimately all of us have a duty to work with the media, the government and the rest of industry to continue to promote safe surfing", he said.
Although the survey showed 92% of parents thought accompanying children online was best, Mr Carr emphasised steps need to be taken to ensure parents are actually supervising children.
Other studies have shown less than a third of parents do actually sit with their children while online, he said.
Recent research suggests parents also need to be careful in balancing supervision with respect for their children's privacy.
Children value privacy and liken over-monitoring by parents to having their pockets searched, Professor Sonia Livingstone from the London School of Economics has found.
Too much intrusive supervision meant many children Professor Livingstone spoke to responded by hiding activities to outwit parents.
The NOP poll coincides with Parents Online Safety Week, with events taking place all over the country to reinforce safety guidelines.