Hire Purchase enables you to purchase assets over a set period of time usually upto 5 years with fixed monthly payments to enable your business to budget and conserve cashflow. The deposit and the period of the agreement can be tailor made to suit the customer's cash flow and monthly budget requirements. At the end of the agreement a nominal option to purchase fee is paid with your last payment and title in the asset is passed to you.
From a tax perspective you are able to claim the relevant capital allowances that are applicable to you and the interest that you pay is all tax allowable. The asset will also show as an asset owned by your business in your annual accounts.
Lease Purchase has all of the advantages of Hire Purchase but it is often used to fund prestige cars where the customer can reduce their monthly payments by choosing to pay a 'balloon payment' at the end of the agreement. Broadly speaking lease purchase is the same as a PCP for prestige cars but it should be noted that at the end of the agreement the customer has a commitment to pay the 'balloon payment' wheras with a PCP the responsibility lies with the funder.