A finance lease transfers most of the risks and rewards of the asset to you without transferring ownership, and under current UK accounting practice it is generally recognised on your balance sheet — an asset alongside a lease liability. Rentals are split between reducing that liability and an interest charge, with depreciation booked separately. An operating lease is usually treated as a simple rental expense.
The distinction between a finance lease and an operating lease is a judgement based on the substance of the agreement — the length of the term against the life of the asset, who bears the residual risk, and what happens at the end — rather than what the document is called. Two contracts with similar names can be classified differently.
The rules on lease accounting have been reformed for some reporting frameworks, with more leases being brought onto the balance sheet. Which treatment applies depends on the standard your accounts are prepared under and on your accounting period, so ask your accountant which framework you report under before assuming an outcome.
That classification has knock-on effects beyond the accounts: it can move your reported assets, your liabilities and your gearing, which matters if you have bank covenants or are about to apply for further funding. Flag any lease to your accountant early rather than at year end.
This is general information, not tax advice. Confirm your own position with your accountant or HMRC.