How can I get arcInfo to understand LOAC so it calibrates coordinate systems correctl

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So I downloaded some data from the 2011 UK Census and I want to add it as a layer on my basemap.

I couldn't see it on the map although it was in the Contents tab in arcmap, so I zoomed out to full view and saw that it was way off. There must be a mis-match in coordinate systems between the basemap and the Census data.

The basemap is using the GCS_WGS_1984 coordinate system and I don't know what coordinate system the Census data is using but it uses the London Output Area Classification (LOAC) which has the features 'areas' and 'subareas' but no coordinates in it's data file. LOAC site

Does anyone know what I can do from here to get the basemap and Census data to understand each other coordinate-ly ?

I found this potentially helpful file but don't know what to do with it as this is my first day playing with GIS software.

Any ideas are very much appreciated. Thank you



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