You need to establish if you have a lease or Personal Contract Purchase (PCP).
A lease is basically a long rental agreement. You never own the car, although most leasing companies will give you a figure to buy the car at the end of the lease. Don't assume this is competitive - sometimes it is, sometimes it's way off. I know someone who wanted to buy a car they had on lease and went and bought it auction about £2k cheaper than the lease company quoted to buy it.
Generally with a lease you won't have the V5 registration document, and the lease company will deal with the road tax. They used to just post the tax discs out shortly before the tax was due, not sure what they do now discs have gone.
If you have a PCP this gives you a greater range of options. From your description, it sounds more like you have a PCP. A PCP will give you a Guaranteed Minimum Future Value (GMFV) on the agreement, sometimes called a balloon payment. This is the amount of the finance that you don't have to make repayments against during the agreement, although you are charged interest on it.
Your options are pay the GMFV and own the car. From the figures above I would estimate your GMFV would be around £4300. Given you're going to have to find north of £2k for a deposit for a replacement, this doesn't look a bad idea. The rate of depreciation on a small car will tail off quite sharply after the first 3 years, so if you buy the car and run it for another 2 years this won't cost you much in depreciation at all - probably hundreds rather than thousands.
You could pay the GMFV and sell the car privately. You need to find out what it would be worth as a private sale to decide if this is worthwhile.
You can use the equity as a part exchange/deposit against a new car. Don't assume the dealer is going to do you any favours here. There are several places a dealer will try and profit from the situation:
The dealer knows what your GMFV is and that anything they offer you above this is a bonus for you, so they can lowball you on the part exchange value.
The dealer knows what you've been paying both deposit and payments, and they will try and creep these up a bit as most people expect prices to rise over time. This might mean you end up paying a higher rate of interest and the dealer gets more commission on the sale of the finance agreement. Often they make more on the finance than they do on the car.
Dealers love PCP's because they know in 3 years time most customers will be back with a problem around what to do and that gives them a great opportunity to sell another car and take a commission on a finance agreement.
Finally, you can hand the car back and walk away - although if the car is worth significantly more than the GMFV, this is a silly thing to do.
You are under no obligation to stick with the same dealer or manufacturer when changing cars on PCP, so shop around. If you like the Up, get down to a Seat and Skoda dealers and see what they'll do you on a Mii or a Citigo.
You got a pretty good deal on the PCP last time around - there may well have been a VM promotion on, but on deals like this the GMFV will be carefully calculated to bring it as high as possible without undue risk to the finance company in order to keep the monthly payments low. This will never give you much equity in the car, so it was always the case you were going to have to find a deposit of around the same again when you came to change. I bet the dealer didn't explain that to you though!
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