No. Once you changed it you're stuck with Dinars.
This isn't correct.
Pretty much every currency exchange in Belgrade makes its living from exchanging dinars (RSD) to Euro and vice versa. Serbian people pay for a lot of things in euro - rent, services, etc. - so it's an everyday thing. The country would grind to a halt if people couldn't exchange their RSD for EUR.
The "hole in the wall"-type exchanges are called Menjačnica. They generally have very competitive EUR/RSD rates (better than the banks). There are dozens of them in the centre of town, most with rates displayed outside. The closer you get to Knez Mihailova (the main pedestrian street), the worse the rate. Shop around, go for the best one. Check the mid-market rates on the xe.com currency site or app.
GBP/RSD rates are considerably worse than EUR/RSD. So if you must take cash, take EUR. I'd use an ATM.
But you shouldn't need much cash these days. Most places take cards. Even many taxis take plastic, though you should check this before you start the journey.
Talking of taxis, always best to call one rather than pick one up off the street. There are fake taxis around the main tourist and nightlife areas - and their meters, if they run at all, run very fast. Real taxis have a number plate ending with TX.
This company is probably the best for English-speakers:
http://naxis.rs/en - they also have a smartphone app.
As already pointed out, at the airport, there is a desk for taxis - as you come through the arrival doors, walk straight ahead and you will see it. They will give you a ticket - but you pay the driver directly. 1800 RSD to the city centre, flat rate.
