One of those present, who did not wish to be named, said: "Some of the members think there was not sufficient consultation as to whether we want a new senior rabbi at this stage. Some queried the bringing over of a candidate who was unknown to the members.
"In the past, senior rabbis have been appointed from junior rabbis who worked with us for many years."
He added that he had no objection to Rabbi Bassous - who heads a Sephardi congregation in New Jersey - but reported disquiet that members were not being given enough time to decide.
Rabbi Bassous is due to arrive in three weeks for an intensive four-day visit to the community's four London congregations, beginning with a "shiur and shawarma" session for young adults at Lauderdale Road.
Following his visit, members of the congregation will be asked to make up their minds about his appointment at a special meeting on December 1. He will need to secure two-thirds of the vote to succeed Rabbi Levy, the leader of the congregation for more than 30 years, who is now 72.
Mr Musikant said the vote had been put back four days from the original date to allow members more time - although that had been decided before the meeting at Mr Sacerdoti's home.
He also pointed out that ordinary members of the congregation had been invited to join the selection panels which interviewed candidates.