"The outcome of the meeting represents a clear vote of confidence in the trustees," he said. "We need to put our new, modernised governance structures to good use.
"We remain in a period of rapid change, and this is often unsettling," he added, following the vote of no confidence in the board of trustees (HW, 24 July).
The vote was triggered by anger over the dire financial state of the institute. But the vote of no confidence was rejected by 489 votes against 210.
Williamson said cutting staff numbers and expenditure had "stabilised" finances, but strategic priorities would be reviewed to prepare for next year's budget.
"We need to move on from the divisiveness that occurred as a result of the tough but necessary decisions we had to make to re-balance the budget."
He said at a time of reduced staff capacity, volunteer input at the Landscape Institute was more critical than ever.
"The branches are collectively the institute. The more that members get involved at branch level, the more connected and stronger will be the whole organisation."
Meanwhile, the Landscape Institute is due to launch a position statement on housing around autumn, which will focus heavily on public housing.
Policy director Paul Lincoln said social-housing groups had a wider social remit than private developers. Projects by the likes of the Peabody Trust were often winning awards for sustainability, he said.
Subscribe to Horticulture Week for more news, more in-depth features and more technical and market info.