I'm not sure why they're open?
It's a UK BT Infinity router.
Best way to find out if I've been hacked?
I'm not in the UK, so never used a Netfinity router, but this probably does not mean you have been hacked, although it might indicate your ISP has (but its unlikely) !!! It is probable that ports 161 and 8081 are open on the router itself - maybe for your ISP to monitor traffic on the router. In the case of port 161 this definately makes sense as 161 is SNMP management. Similar 8081 could allow people from BT to log in and modify your router.
If you are able to reach the ports INTERNALLY I would not be worried. If you can access them externally, try unplugging the LAN devices and disabling the WIFI (or stop using it at least) and see if these ports can still be accessed remotely. If they can, bitch to your ISP that those ports should not be open to the world (or if you can, simply turn off those services on the router itself)