A neo-Nazi group is to become the second extreme rightwing outfit to be banned as a terrorist organisation in the UK, the home secretary has announced.

Sonnenkrieg Division (SKD), members of which have been jailed for serious offences, is to be proscribed, making membership of the group illegal and punishable by up to 10 years in prison, Priti Patel said.

Another order will recognise the extreme right wing group System Resistance Network as an alias of the already proscribed neo-Nazi organisation National Action.

Two teenage members of SKD, Michal Szewczuk, 19, from Leeds, and Oskar Dunn-Koczorowski, 18, from west London, were jailed for terrorism offences in June last year.

The pair encouraged an attack on Prince Harry, who they referred to as a race traitor for marrying Meghan Markle, a woman of mixed race, glorified the Norwegian mass murderer Anders Breivik, and said white women who date non-white men should be hanged.

The orders come less than a week after nine people with immigrant backgrounds were murdered in the western German city of Hanau by Tobias Rathjen, a 43-year-old who had posted a racist video and manifesto on the internet.

Patel said: “Recent attacks here and in Germany have highlighted the threat we continue to face from violent extremism.

“We are working to keep the public safe by increasing funding for counter-terror police and strengthening the law to keep terrorists locked up for longer.

“By proscribing these groups we are making it much harder for them to spread their hateful rhetoric.”

This decision follows a meeting of the Proscription Review Group, which brings together representatives from the police and other partners to assess the risk posed by groups that may be considered for proscription.

SKD is the UK arm of the neo-Nazi Atomwaffen Division formed in 2015 in the southern US. It emerged in 2018 around the time of the arrests of Szewczuk and Koczorowski.

According to the anti-racist group Hope Not Hate, SKD was heavily influenced and obsessed by Satanism and extremist Muslim ideology, which forms the basis of the so-called “white jihad” ideology, the spiritual component that encourages neo-Nazis to kill and die “for the cause”.

The move to ban SKD comes amid evidence suggesting far-right violence is on the rise across the UK.

Senior counter-terrorism officials have warned that the far right poses the fastest-growing terrorist threat in the UK.

A quarter of all terrorism arrests in the past year were linked to far-right violence and the far-right caseload of counter-terrorism police jumped from 6% to 10% in two years. Counter-terrorism officers have foiled eight far-right terrorist plots since March 2017.

Of the 5,738 referrals to the government’s anti-radicalisation programme, Prevent, 1,389 or 24% were referred for concerns related to right-wing radicalisation, up from 18% in the previous year, and 10% in the year to March 2016.

In a paper written for the commission on countering-extremism, the academic Joe Mulhall said far-right demonstrations had grown to sizes not seen since the 1930s.

Police forces do not record far-right incidents but they do record terror-related offences and hate crime, the latter of which has risen sharply.

The most recent official statistics on hate crime show that in 2018-19, there were 103,379 hate crimes recorded by the police in England and Wales, an increase of 10% compared with 2017/18. The majority of hate crimes were race hate crimes, accounting for about three quarters of offences (76%; 78,991 offences).

The Home Office said the increase was largely driven by improvements in police recording, although there were spikes in hate crime following the EU referendum and the spate of terrorist attacks in 2017.

The most high-profile cases of far-right violence in recent years were the murder of the MP Jo Cox by the white supremacist Thomas Mair and the foiled plot to kill the MP Rosie Cooper by Jack Renshaw, a former member of National Action.

Stephen Doughty MP, member of the House of Commons home affairs select committee, said he had repeatedly called for bans of both SKD and System Resistance Network.

He told the Guardian: “This is a very welcome but hugely overdue decision. I and others – including journalists and organisations like Hope Not Hate – have repeatedly urged tough action on these sick, twisted neo-Nazi organisations for the last few years.

“Yet despite repeatedly meetingministers and officials in private and raising concerns in public it has taken until now for them to be banned.

“The government need to wake up to the threat posed by these extreme right organisations - who would seek to target communities from Muslims to Jews, the LGBT community and anyone who doesn’t meet their white supremacist criteria.”

