If I mine bitcoin, would it count as income in the UK? If so, would I have to declare the value of my bitcoin on any forms which ask for how much money/income I have?
Yes you would.
Bitcoin is a form of property right or asset, just like any other form of wealth. And, income is a positive increase in the sum total of your property rights. You might be able to take deductions in connection with whatever you parted with in order to obtain a bitcoin, depending on the transaction, just as you might be able to take a deduction for inventory expenses associated with income in the form of money.
HMRC "does not consider cryptoassets to be currency or money" but sees them as having economic value because "they can be 'turned to account' - for example, exchanging them for goods, services, fiat currency (that is money declared by a government to be legal tender) or other tokens". They are "a new type of intangible asset".
Individuals are liable "to pay UK tax if they are a UK resident and carry out a transaction with their tokens which is subject to UK tax". They are liable for "Income Tax and National Insurance contributions on cryptoassets which they receive from their employer as a form of non-cash payment [or from] mining, transaction confirmation or airdrops." - HMRC cryptoassets for individuals