Has it not got WiFi anyway
This.
Can I simply buy a router, see below
“Simply”? No. The router out-of-the-box will expect to route to and from the ADSL connection, not an external router.
If you need a router then something that pertains to be for ‘cable’ connections should work; however, if all you need is a WiFi connection and assuming the Orange box has a spare Ethernet connection, you just need a wireless access point. In keeping with your first link, something like http://www.amazon.co.uk/TP-Link-TL-WA701ND-150Mbps-Wireless-Access/dp/B002YETVVE .
However, as mentioned, I’d be surprised if the Orange router didn’t do it already. Before you buy anything, it’d help if you could clarify exactly what you’ve got already, make / model number rather than “thingy”.