Is there a way of converting Ordnance Survey NTF data to QGIS that will correctly import the data and build polygons?
QGIS will read the data as is, but it imports the polygons only as centrepoints.
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You can use the open source tool GDAL which has a command called ogr2ogr which can convert NTF files into a range of vector formats, either using the various language bindings (including python) or at the command line.
FME can also read NTF files so a custom workbench could be created to read in your files, perform any initial processing, if required, and then convert them to whatever format you need. FME is not free, but you can get a free trial which would support your needs in the short term.
NTF to MIF is a free translator available from here - http://www.bodley.ox.ac.uk/guides/maps/translat.htm
for Shapefile use GDAL see Converting MapInfo TAB and/or MIF to SHP using free tools or ArcGIS for Desktop core product?
This will only convert to lines - so there will be another post-process required afterwards to build polygons.
Either convert to shapefile or postgis and build polygons using numerous tools in QGIS to do this Geoprocessing tools with help with that.
Depending on the size number of NTF files needing to be converted it might be better to use postgis. Then use ST_BUILDAREA https://postgis.net/docs/ST_BuildArea.html