The demolition team, Jurgens Contractors, did not respond to calls from the Chronicle, and builder David Corney would not comment.
Wanganui Mayor Annette Main said Mr Efstratiou was demolishing the buildings at 83-97 Victoria Ave, except for the front facade of number 83 and most of number 87.
The demolition is happening under a resource consent granted in March 2012. It also allows Mr Efstratiou to rebuild a development. As a condition of the consent, he has to rebuild along the Victoria Ave frontage within six months.
Ms Main said the six months would be counted from when the council issued a code compliance certificate under the Building Act, and council would monitor the rebuilding efforts.
She welcomed the latest development.
"It is great to see work under way which will eventually result in a new development in the central city," Mayor Main said.
"There has been community concern about the lack of activity on the site, so it's pleasing to see some progress being made."
Wanganui District councillor Michael Laws feared "another gaping hole will be left in the city's streetscape".
"This time, it will be slap bang on the main street. It will look dreadful and poorly advertise our wonderful city to visitors and potential businesses alike."
The Victoria Ave buildings that are coming down have been vacant for some time.
Mr Efstratiou's brother-in-law, Nigel Auret, has ownership interests in the lower storey of the Perrett Building at the western end of them. The Chronicle understands there was a minor boundary issue between the two owners. Mr Auret said he could not comment on anything.