Usually yes. Under hire purchase you are treated for tax purposes as the owner of the asset from the outset, even though legal title only passes when you make the final payment. That means qualifying plant and machinery bought on HP can attract capital allowances on the capital cost, and the interest element is treated separately as a business expense.
Timing is the detail people miss. The rules generally require the asset to be brought into use in your business before you can claim, and the claim is on the capital cost of the asset — not on the total of the payments, which includes interest and fees. So the figure your accountant uses is not the number on the agreement schedule.
Whether the full cost can be relieved immediately depends on which allowances are open to you in that period — the Annual Investment Allowance, or any first-year allowance in force at the time — and on how much of your allowance you have already used. Anything not covered goes into the relevant pool and is written down over time. Your accountant can confirm what applies to your accounting period.
Some assets are treated differently — cars especially, and certain second-hand or leased-on items. Lease purchase and other balloon-based agreements often work the same way as HP for allowances, but you should not assume it from the product name alone. Send the agreement to your accountant before you file.
This is general information, not tax advice. Confirm your own position with your accountant or HMRC.