Actually I finally fixed it, by following this video:  Then I managed to do Remove Device from Devices and Printers (it continued to show there greyed out but had gone, not apparent until I clicked the refresh arrow), then added it again with Add Device and it then worked.
This morning my Microsoft Bluetooth Mobile Keyboard 6000 which previously was working fine has stopped working with my XPS 13 (9350, running Windows 10). The keyboard is greyed out in Devices and Printers. I've tried Remove Device from there but it won't go. I've tried adding it again as a new device but it isn't detected. Moreover the Microsoft help says that Bluetooth should be listed in Start>Settings>Devices but there is nothing about Bluetooth in there, which makes me wonder if Bluetooth has stopped working entirely. I have the latest Windows Updates, Dell updates and BIOS. I've updated drivers using Driver Reviver (though not certain this always updates them all) and also the relevant-looking Bluetooth drivers in Device Manager; only one was out of date but it made no difference. Also rebooted several times during all of this. What should I do?
Bluetooth keyboard stopped working on Dell XPS 13 (9350)