Edit:
When disconnecting the Ethernet cable the wifi works again. As far as I can tell it is due to the default route of the Ethernet (thanks softweyr), however I am still unsure as to how to solve this. In "route -v" it shows:
Kernel IP routing table
Destination Gateway Genmask Flags Metric Ref Use Iface
default 192.168.1.1 0.0.0.0 UG 202 0 0 eth0
default 192.168.1.8 0.0.0.0 UG 303 0 0 wlan0
192.168.1.0 0.0.0.0 255.255.255.0 U 202 0 0 eth0
192.168.1.0 0.0.0.0 255.255.255.0 U 303 0 0 wlan0