Can anybody help me with identification of this very thin hose and what it does? (Mine has split because I am a ham fisted gimp)

Click image to enlarge

Click image to enlarge

It's one of the vacuum hoses, if you can get the broken bit out of the flexi using fine nosed pliers and a bit of heat (I used a small drill bit to get the last few bits out, just by hand, not with a power tool) you might be able to push the rigid pipe back in, they have a bit of stretch in them.

Thanks for the info - I will certainly try this! Don’t suppose you have any info around what it does??! 2007 Range Rover Vogue 3.6 TDV8

The back hose goes to the air filter, the broken one goes to a little block under the turbo hose and coolant hose, no idea what it's function is, there is an electrical connection on top and the vacuum hose disappears down the front of the engine.
Sorry I can't be of more help

Awesome - have reconnected and all is well. Thanks for the help! 2007 Range Rover Vogue 3.6 TDV8