Buying equipment outright turns a productive asset into a hole in the current account. Asset finance spreads the cost over the period the asset actually earns, and the security is the asset rather than a charge over property or a personal guarantee against your home.
The structure decides what you end up owning. Hire purchase is a route to ownership: you pay a deposit, then instalments, and the asset is yours at the end. A lease is a route to use: payments are for the use of it, and at the end you return, extend or sometimes buy. Which is right turns on whether the asset holds value and whether you want it when the term ends.
Term is set by the asset, not by you. Heavy plant with a long working life supports a longer agreement than IT equipment, which a lender will want repaid well before it is obsolete. Ask for a term the asset does not support and the answer is no, or a much larger deposit.
Hire purchase against lease, on your numbers
The comparison is not the monthly payment. It is the total cost, what you own at the end, and how each is treated in your accounts, which is a conversation to have with your accountant before signing rather than after.
New, used and private sale
Most lenders fund new and dealer supplied used equipment readily. A private sale or an auction purchase is a shorter list and usually needs an inspection, so it is worth establishing before you bid.
Refinancing what you already own
Equipment bought outright can often be refinanced to release the cash back into the business. It is an often overlooked route to working capital, because the security already exists.
Balloons and what happens at the end
A balloon payment lowers the monthly cost and leaves a sum due at the end. That is fine where the asset holds value and a problem where it does not, so the exit is agreed at the outset.