Here's the solution I've found, since it doesn't look like neutron router-update allows this manipulation, I've resorted to using the REST API. With the Keystone token in $TOKEN, assuming RRR is the router's UUID, NNN the public network's and SSS the subnet thereon:

# Let's get the router's current config
curl -H "X-Auth-Token: ${TOKEN}" http://10.10.0.101:9696/v2.0/routers/RRR | python -m json.tool > /tmp/xxr
# Edit the output (/tmp/xxr) leaving just the sub-structure we want to alter (here I changed the IP address):
cat /tmp/xxr
{
    "router": {
        "external_gateway_info": {
            "network_id": "NNN",
            "enable_snat": true,
            "external_fixed_ips": [    
                {
                    "ip_address": "10.10.3.1",
                    "subnet_id": "SSS"
                }
            ]
        }
    }
}
# Let's apply it:
curl -XPUT -H "X-Auth-Token: ${TOKEN}" http://10.10.0.101:9696/v2.0/routers/RRR -d @/tmp/xxr
# finally let's check the change has been applied to both the router and corresponding port:
neutron router-show RRR
neutron port-list | grep 10.10.3.1

(don't forget to substitute your Neutron end-point URL and you should be good).

If you know of a less hacky solution, please do contribute!