I'm trying to load up a set of shapefiles in QGIS, to undertake a points in polygon analysis. I load up the points in OSGB 1936 / British National Grid (EPSG: 27700) (the same as the polygons), however they do not appear. I've enabled 'on the fly' transformations. See a screenshot below with no visible points layer:

[![][1]][1]

I've opened another project with the points in WGS 84 and then saved them in the transformation required (EPSG: 27700). Still no luck. 

I then opened them in Arcmap and they worked fine, see below:

[![enter image description here][2]][2]

I'm all out of ideas, are there any other suggestions for how to get this working in QGIS?

EDIT: See the requested metadata for the points layer below:

    General
    Storage type of this layer
    ESRI Shapefile
    Description of this provider
    OGR data provider (compiled against GDAL/OGR library version 2.0.2, running against GDAL/OGR library version 2.0.2)
    Source for this layer
    C:/Users/ejo31/Desktop/cell.ID.locations/open.cell.id.27700.shp
    Geometry type of the features in this layer
    Point
    The number of features in this layer
    1332599
    Capabilities of this layer
    Add Features, Delete Features, Change Attribute Values, Add Attributes, Delete Attributes, Create Spatial Index, Fast Access to Features at ID, Change Geometries, Presimplify Geometries, Presimplify Geometries with Validity Check
    Extents
    In layer spatial reference system units
    xMin,yMin -99.7747,-44.7261 : xMax,yMax 174.781,76.6116
    Layer Spatial Reference System
    +proj=tmerc +lat_0=49 +lon_0=-2 +k=0.9996012717 +x_0=400000 +y_0=-100000 +ellps=airy +towgs84=446.448,-125.157,542.06,0.15,0.247,0.842,-20.489 +units=m +no_defs



  [1]: https://i.sstatic.net/sUOUp.png
  [2]: https://i.sstatic.net/jUuuV.png