It seems the layer's CRS is not correctly recognized. When loading the layer to an empty project, I get the same error you describe in the comments.
To solve it, proceed as follows:
- Create a new, empty project
- Load an OpenStreetMap basemap form XYZ tiles
- Drag and drop the layer to QGIS
- Right click layer > Layer CRS... > Set Layer CRS.... In the dialog window that opens, select British National Grid
EPSG:27700.
Then the layer appears in the correct place. I exported this layer again in EPSG:27700 as well as in Web Mercator EPSG:3857 - you both layers + project file can be downloaded here.
Be aware: normally, don't change the layer's CRS, see here and here why and for some background.
Here how it looks when loading the initial layer: both layer's CRS and project CRS are unknown or unnamed:

When you load the initial layer you linked to an empty QGIS project, the project CRS will be undefined as the layer's CRS is not recognized and QGIS uses the CRS of the first loaded layer to define the project CRS. So from there, you got a whole bunch of problems. That's why in such cases always load a background layer first. You can always change the layer CRS later by clicking the icon at the bottom right of your QGIS window.