HMRC administers UK taxes and publishes the manuals that describe how trading profits are characterised. For most UK individuals, share and derivative profits fall under uk-capital-gains-tax, while uk-spread-betting-tax profits are generally outside both capital gains and income tax because the activity is treated as a wager.
Unlike the US system, the UK does not routinely receive a transaction-level information return from your broker for domestic accounts, so accurate records are your responsibility. Self assessment deadlines and the requirement to report gains above the annual thresholds both sit with the taxpayer.
This is general information, not tax advice. UK rules change frequently, allowances are cut and restored, and the treatment of any particular activity depends on your facts, so take professional advice.