Two teenagers suspected of alleged extreme right-wing terror offences will appear in court in London on Friday, with police saying they both face "extremely serious charges".

Metropolitan Police said that an 18-year-old man and a 19-year-old woman were charged on Thursday following a "proactive investigation" by its Counter Terrorism Command unit.

Rex William Henry Clark of Ilford, east London, was charged with the preparation of terrorist acts, contrary to the 2006 Terrorism Act.

Police charged Sofija Vinogradova of Cheshunt, north of London, with preparation of terrorist acts and two counts of collection of information likely to be useful to a person committing or preparing an act of terrorism.

Both are in custody and will appear at Westminster Magistrates' Court on Friday. 

Police said the investigation "is related to suspected extreme right-wing terrorism activity."

"These are extremely serious charges, but I would urge the public not to speculate any further about this case at this time and allow the criminal justice process to run its course unimpeded," said Commander Dominic Murphy, Head of the Met's Counter Terrorism Command.

"I want to reassure the public that at this time we do not believe that there is any wider threat related to this investigation, although our investigation very much continues," he added.

Far-right riots recently broke out across England and Northern Ireland following the stabbing to death of three girls at a dance class in Southport, northwest England.

Murphy said that the investigation had not come about "as a consequence of the disorder across the country which occurred following the terrible events in Southport."

Police initially arrested the woman on August 4 on suspicion of being in possession of a firearm.

She was bailed but arrested again on August 10. The 18-year-old man also arrested at the same address and both were taken to a London police station.