A:Answer Yes, it will work just fine. This is the Bluetooth model of the Frontier and does not support non-tethered access to a cellular network. It will pair to a compatible phone regardless of the network it's on, though.
The only potential issue is the charger, which will have a US-style plug for power. I believe the charging base uses a USB connector, though, so it should plug into a UK-compatible USB charger.