I think you can probably ignore the mintage figures. This was the final year of the large 10p's, outside the BU and proof sets. My thought is that the Mint overestimated demand and minted far more than ever got issued; possibly a large proportion of the strike was melted down?
Michael Gouby has a couple of high grade currency examples for sale at high prices. Certainly, you don't see 1981s offered for sale otherwise, so they are presumably much rarer than the mintage suggests.
Other rarities include the very rare 1983 NEW PENCE 2p, and supposedly recent 50p's such as Kew Gardens (not as rare as thought, really), the 2012 Olympic 'swimmer' 50p with the waves across the swimmer's face, the 2008 'no date' 20p though again, its rarity is exaggerated. I don't think the 1981 10p is possibly as rare as those, but it's telling that the ones on sale on eBay are all proofs (even the one described as BU UNC) and cost between £15 and £18, which is far more than proofs of other years.