I will be selling products from a web site which are directed at pet owners. The nature of these products will mean ingestion or dermal application and as such represent a biosecurity risk and cannot therefore be resold. I will not be able to guarantee the hygiene circumstance the product has been exposed to whilst in the possession of the consumer. I propose to apply a policy that we cannot accept returns, is this allowed?
There is no special exemption for such goods from the "right to cancel" rules of the Distance Selling Regulations.
Regulation 13(1) contains certain exemptions from the cancellation provisions, including in relation to "goods ... which by reason of their nature cannot be returned". I think that this exemption would be construed narrowly and would probably not cover the goods you describe. If you search for those words on Google, you'll see that many traders do however take a more liberal view of the scope of this Regulation.
13(1) also includes an exemption for goods which are liable to deteriorate rapidly, which might apply to some of the things you sell.
Customers who cancel contracts under the Regulations do have an obligation to take reasonable care of the goods. You could argue that, if the use of goods makes them unsaleable, then taking reasonable care means not using them. However, this doesn't really help if you are unable easily to tell whether goods have been used.
If the Distance Selling Regulations often seem unfair to traders, that is because they were never meant to be fair. The underlying policy goal is to promote ecommerce across the EU, the idea being that all traders affected by the rules would benefit from an increase in distance sales.