On Wednesday, 17 April 2019 11:19:28 UTC+1, Roger Mills wrote:
The prescription specs which I use for computer-based activities have a
scuff mark about the size a finger-print from a little finger on one of
the (plastic) lenses.

Whilst I could buy a new lens for £30 or so, I've been trying to polish
it out on a DIY basis.

I tried Brasso but didn't do a lot because the blemish was a bit too
deep. I then rubbed the area very gently with very fine wet & dry, used
wet. This got rid of the scratches, but left the area looking like
frosted glass. I've improved it quite a lot by buffing it with a
dremel-like tool, using a buffing paste made from olive oil and talcum
powder (how DIY can you get!) followed by a further application of
Brasso. The affected area is still a bit blurry.

Any ideas of what else to try?

The"proper"stuff to use is"jeweller's rouge.

https://www.ebay.co.uk/i/132360934221?chn=ps

Ultra fine abrasive. Used on watch glasses.