The rise in the number of children being investigated for terrorism in the UK is “staggering”, the boss of MI5 said, as he warned of “canny online memes” drawing them into extreme right-wing ideologies.

Director general Ken McCallum said the security agency was seeing “far too many cases where very young people are being drawn into poisonous online extremism”.

Speaking at the Counter Terrorism Operations Centre in west London on Tuesday, he said: “Sadly, 13% of all those being investigated by MI5 for involvement in UK terrorism are under 18.

“That’s a threefold increase in the last three years. Extreme right-wing terrorism in particular skews heavily towards young people, driven by propaganda that shows a canny understanding of online culture.”

Answering questions from reporters, he said the proportion – one in eight of the people MI5 was investigating for involvement in UK terrorism – was “quite a staggering thing”, adding: “That’s not something I would have expected to see earlier in my own career.”

Reiterating concerns he previously raised about the role of the internet being the “biggest factor” driving the trend, he described how easily youngsters could access “inspirational and instructional material” from their bedrooms.

Most are influenced by a range of extreme right-wing ideologies, he said, adding that “canny online memes” were drawing children into such views.

“It’s not really a consistent single ideology on the extreme right-wing side, and that is what has skewed the numbers most heavily,” he said.

A record number of child terror suspects are being arrested, Home Office figures published last month show.

Police detained 242 people on suspicion of terror offences in the year to June. Of these, 17% (40) were aged 17 and under.

This is up 60% from the 25 detained in the previous 12-month period, and is the highest number since records began more than 20 years ago, when just two children were arrested in the year to June 2002.

It means children are now the second largest age category for suspects being arrested for terrorism. The 118 people aged 30 and over who were detained in the year to June make up the largest age category, accounting for 49% of arrests.

Mr McCallum previously said extreme right-wing terrorism was “sadly here to stay” as he told how agents had been investigating teenagers as young as 13.

According to separate Home Office data published last year, children aged 10 and younger are being reported to the Government’s anti-terror programme, Prevent.

The latest figures on referrals to the scheme, which aims to stop people turning to terrorism, also set out how children aged 14 and under now account for the second largest proportion of potential cases.

The more detailed analysis on the ages of children being referred to Prevent in response to “public interest”, the Government department said.

In the year to March last year, there were 6,817 referrals to Prevent, up 6% on the previous year when 6,406 were recorded.

This is the third highest number of referrals since records began in 2015/16 and is being driven by reports from teachers and police, among others, the Home Office report said.

Some 256 referrals, where age is recorded, were for children between zero and 10 years old. Those aged between 11 and 15 accounted for 2,628 (39%) of referrals to the programme.

People aged 15 to 20 accounted for the largest proportion of referrals (2,203; 32%). But those aged 14 and under were the second largest (2,119; 31%).

The age was known for 6,796 of the referrals in the period.

As with previous years, the majority of referrals were boys and men, accounting for 90% out of the 6,801 cases where gender was recorded.