Is the region set correctly? Potentially you could make the purchase on the computer, then find it in your purchases on the Apple TV, but that ought not to be necessary.

tt2

if it's a movie you added from an external source to iTunes then because iTunes on your computer can play it does not mean the appletv can it has to be in a compatible format

Video Formats

H.264 video up to 1080p, 60 frames per second, High or Main Profile level 4.2 or lower

H.264 Baseline Profile level 3.0 or lower with AAC-LC audio up to 160 Kbps per channel, 48kHz, stereo audio in .m4v, .mp4, and .mov file formats

MPEG-4 video up to 2.5 Mbps, 640 by 480 pixels, 30 frames per second, Simple Profile with AAC-LC audio up to 160 Kbps, 48kHz, stereo audio in .m4v, .mp4, and .mov file formats

I realize I skipped over this sentence and assumed you were talking about content in the iTunes Store, not your library.

Am mirroring from my phone to watch chosen film,,,

If the content is in your iTunes library you ought to be able to play it in iTunes and tell iTunes to send the output to the Apple TV, or alternatively get the Apple TV to look at the iTunes Library and play what is there.

tt2