How do I ensure a clipped raster matches the cell alignment of the Input Raster?

[JamesArmstrong2]

I'm trying to clip an input raster to a 16 x 16km AoI. Whilst I can easily clip to the AoI using 'Clip Raster', the cell alignment of the output raster is always significantly different to that of the input raster (see image. The purple line is the corner of my AoI).

I need the cells to be close to, if not perfectly, aligned as I will be later using the imagery for Forest-based classification of landcover. 

I've tried using the 'Snap Raster' Environment, with my input raster as the snap raster, however this changes nothing of my end result.

I've also tried to align the output extent with the cells of the input raster, however I cannot find an accurate way to do so.

Input Raster / Snap Raster - Sentinel-2 image, 10m spatial resolution, reprojected from WGS 84 to British National Grid.

Output Extent - 16 x 16km square, single polygon feature class, British National Grid. Not aligned with the cells of the input raster.

My map frame is also using:

Projected Coordinate System - British National Grid

Geographic Coordinate System - OSGB 1936

[DanPatterson]

You can "fix" the extent, but I might advise against it since resampling of the original raster may be necessary to have it fit into the extent.  You will have to weigh potential changes to the input raster versus altering the extent... which is more important?

[DavidPike]

That's very strange the snap raster isn't being honoured.  Maybe another environment overriding it?

How about extract by mask or right-click->data->export raster?