Using two routers to connect to work laptop

Hello,

I recently signed for Virgin broadband having moved house and got a new netgear modem. My work laptop has a tight security system for working from home and needs to be connected to the router with a cable. Problem is that is does not work when directly connected to the new netgear router. It does work if I take an ethernet cable from the virgin netgear router to my old router (speedtouch st585 v6) and then a further ethernet cable to my laptop. Complicated!

Ideally I would like to not have to sit right next to the modem, so would love to get my two routers to connect wirelessly, then sit in my office with my speedtouch router with an ethernet cable into my laptop.

Is there any way of doing this!!!?

Many thanks!!