The Met Police said the 39-year-old man was arrested at an address in London; while the 68-year-old man was arrested in Powys, Wales and the 43-year-old man was arrested in Pontyclun, Wales.
All three have been detained under the Police and Criminal Evidence Act and remain in police custody, the Met added.
As part of the investigation, searches were carried out at locations in London, East Kilbride and Cardiff.
The Met said the three arrests and subsequent search activity were supported by counter-terror police in Wales and in Scotland.
A Police Scotland spokesperson said: “On Wednesday, 4 March, we carried out a search of an address in East Kilbride on behalf of an investigation being led by Counter Terrorism Policing London.”