Whether or not you own the car or van at the end of your lease depends on what type of finance deal you have chosen.
Contract Hire is the most popular form of leasing. If you lease a van or car through Contract Hire, you will not own the vehicle at the end of the lease agreement. Once the Contract Hire agreement is up, you simply hand the car or van back to the finance company, who collect it from you for free. Provided the vehicle is in good condition, you will not pay damage charges. You can then choose a new lease agreement on your next car or look elsewhere.
Personal Contract Hire works in a very similar way. You can drive the vehicle for a set amount of time, but you never actually own it. When a Personal Contract Hire agreement comes to an end, you hand the vehicle back to the finance company.
If you've opted for Personal Contract Purchase, you have the option to take ownership of your vehicle at the end of your lease, by making what is called a balloon payment. This voluntary payment is decided at the beginning of your lease, and allows you to keep the vehicle if paid at the end of your agreement. You do have the option to hand the vehicle back and not pay the balloon payment too.