If you want to keep the car, investigate it. If not, it is not worthy.
Keep in mind that if you decide to sell the car at this point, you will lose a lot and you will make a very happy new owner.
Three year old cars with average mileage (less than 1K miles per month), sell around £10K, which is less than half the price of a new car. Considering the part exchange price, you end up losing two thirds of what you paid for a new car.
There are a lot of heat shields under the car. These rot and start vibrating. It can be something as simple as that.
The safest bet is to inspect the car underneath. Somebody had written that hit something on the road and it started making a noise something but could not figure out what was going on. He called the road assistance which found out a piece of wood stack under the car. They removed that, drove it to the garage without any noises and inspected it only to be found that it was OK. So if you have a road assistance, they may be able to check that for free.
On way or another, if you want to find out what is going on, no matter how many test drives you do, you will do to do a close inspection. And if you cannot do, a trusty garage will be able to sort it out. But do not pay any silly bill if you have no intention to keep the car.