If your business is VAT registered and the asset is used for taxable business purposes, you can generally reclaim the VAT — but the timing depends on the agreement. On hire purchase the VAT on the asset price usually falls due up front and is reclaimed in that VAT period. On leases and contract hire, VAT is charged on each rental and reclaimed as you go.
That difference matters for cash flow. Hire purchase can mean finding a substantial VAT amount at the start, before you have recovered it from HMRC, which is one reason some businesses lease instead, or use short-term funding to bridge the gap. Leasing spreads the VAT across the term rather than removing it.
Vehicles are the big exception. There are longstanding restrictions on recovering VAT on cars: recovery on the purchase of a car, including on hire purchase, is normally blocked unless the car is genuinely used only for business, and only part of the VAT on the finance element of a leased car is typically recoverable where there is any private use. Commercial vehicles are usually treated differently from cars, but the classification is not always obvious, so check it before you sign.
Recovery also depends on your VAT position generally — whether you are on a special scheme, whether you make exempt supplies, and whether the asset has any non-business use. Do not assume the VAT on a quote is fully recoverable until your accountant has confirmed it.
This is general information, not tax advice. Confirm your own position with your accountant or HMRC.