Can I put a higher amp fuse in a wall mounted fused connection unit?
In general, NO. Replacing a fuse with a higher-amp fuse is a very bad idea and can lead to fires. 

Fuses (and circuit breakers) are rated such that they blow or trip before any part of the circuit gets to a dangerous current. You rate the fuse or breaker based on the lowest current rating of all the devices and wires in the circuit .

In your case, the manufacturer of the connection unit determined (somehow) that the "weakest link" in that circuit can only draw 5A before it exceeds its limits. Putting in a 13A fuse would thus allow that weakest link to draw almost 3 times what it may be designed to, which leads to increased heat and then fires. 

There is a reason your fuse is tripping and you need to figure out what that reason is. Perhaps there is a problem with your lamp post, the bulb, one of the sockets, or the van charger. Fix the underlying problem, and you won't have any more blown fuses.