Problem with wired connection seeing devices connected to netgear router

You probably have the Netgear connected to the network via its Internet/WAN port.  For all intents and purposes, anything that tries to communicate through that port is on the Internet as far as the Netgear is concerned.  That's why a wired device cannot see the Netgear control panel.  You have two options for fixing this setup.

If the Virgin modem is truly in bridge mode, then you must not connect any other devices to it other than a router.  All devices must go behind the router.

Internet---Modem---Router---Devices

If it's not practical to move the wired devices behind the router, then the alternative is to disable bridge mode on the modem and enable Access Point (AP) mode on the Netgear.  The setting is under ADVANCED > Advanced Setup > Wireless AP.

Internet----Modem/Router----AP----Wireless Devices
                               |
                               |
                      Wired Devices

If you decide to do this, you can also use re-enable Wi-Fi on the Virgin router.  If you put enough distance between the Virgin and Netgear boxes, you can enjoy expanded Wi-Fi coverage.  You can use the same SSID and Wi-Fi password on both.  Just be sure to use different Wi-Fi channels.