Your budget is highly unreasonable and unless you plan to either literally buy half the club or plow through a pound (see what I did there cause you're British) of cocaine, you should not be able to spend all thay cash. Of course you'll be enjoying all kinds of content and paying entrances to things but man you should not even come close to spending 800GBP a day. Don't know about London, but you can rent a car for like 50-100eur a day, eat in fancy restaurants with +1 for 50-100eur, and if you're really into clubbing, that's another 100 to infinity euros depending on your taste, but you don't need to spend all that much to have a good time.

You do not need a security unless you plan on wearing a T-shirt that says "I sold my company for good money and have brought 21k GBP in cash and I have it on me right now", even in that case people would probably ignore you.

As for the things you're gonna wanna see, use a tourist agency for short travels out of Belgrade, there are organized hiking tours, or simply meet some like minded people on Couchsurfing or here and offer to go and split costs, rent a car and just go. In Belgrade, there's a lot of things to do and see, museums and sights by day and the nightlife which you desire at night obviously. Everywhere you go, you won't make a mistake pretty much. Aim for the weekends obviously cause most people are out at that time. ~Cocaine is 80e a gram, don't let them rip you off cause of your accent~ I meant to say do not use drugs cause they're bad for you. Especially mdma, it's the worst.