Just released in OpenData and as an OS MasterMap form for PSMA members. The data is available to download in GML or ESRI Shape files. Obviously the shape files can easily be grought into MapInfo but do save a copy in native tab format for better performance.
The OS Open Greenspace product provides the location of public parks, playing fields, sports facilities, play areas and allotments, along with access points for entering and exiting urban and rural greenspaces. This dataset covers the whole of GB.
OS MasterMap Greenspace covers urban areas across England, Scotland and Wales. Check the OS website for coverage. At first glance, this looks like MasterMap minus the buildings and roads, with classifications for both Function and Form. There is a facility for PSMA users to report errors!