I cannot comment on UK tax law but in general taxable earned income does not need to be fiat. You could earn anything worth money and that would be taxable income. But if your employer, say, recited poems to you in exchange for your work, that would not be taxable because such an activity cannot be traded for anything else.
It could be argued that Hive is an MMOG. Some countries only tax in-game assets earned on MMOGs when they're cashed out. I don't know about the UK. There are other complexities like how to tax Hive Power earned as rewards. HP is controlled by a smart contract that does not allow it to be cashed out except with a considerable delay. If you asked, you'd be hard pressed to find anyone at HMRC who could give you any definitive answers. I think if you just pay taxes on what you cash out into fiat, other cryptocurrencies or goods or services, you'll be fine. Owing to the complexity and novelty of Hive, that is the only just and fair model of taxation of Hive income. Additionally, your tax authorities would most likely be completely unable to determine the exact amount you owe even if they managed to come up with a theory on how your taxable income should be calculated. For that reason, I don't think publishing detailed reports on your earnings is a good idea.
RE: My Hive stats for last month: not bad at all!