Wheatfield Parks Limited also owns the freehold of Blagdon Water Gardens and a freehold nursery site at Churchill.
The company employed 40 staff, 33 who were made redundant immediately following the announcement.
Ross Connock and Rob Lewis of Price Waterhouse Coopers (PWC) have been appointed joint administrators. They blamed the closure on the economy.
Administrators have closed Blagdon Water Gardens and are holding closing down sales at both Tickenham and Congresbury garden centres, with up to 60 per cent off.
Both garden centres have closed.
At the Congresbury site, the separately-run companies of Heather's Coffee Shop, Mendip Conservatories and the butterfly house will remain open. The coffee shop can now be accessed through the conservatory business entrance