Routers aimed at customers on cable broadband networks (and the original/initial customers of BT Infinity) had a modem that would have a router one could describe as a cable router.
On a "true cable router" there is an RJ45 Ethernet connection for the Internet side (plugs into the cable modem or for BT Infinity the VDSL modem) and then multiple RJ45 Ethernet ports and WiFi on the internal network.
The original BT Homehub they used for Infinity had one of the Internal ports used for the Internet connection to the modem.
You might know some people with spares. I've got my BT one and a Linksys WRT of some sort. There will be some cheap routers described as travel routers that you plug into the Ethernet port in say your hotel room and then get a WiFi hotspot.
Some are versatile and work in multiple modes, eg. (links to a router on Amazon).
goo.gl/tMZbD1
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