Iphone 6 has completely frozen.

It went blank, seemed to switch itself off. Could not restart it, so plugged it in to see if a charge would help (though I had charged it last night and had used it fine earlier today).

I eventually got the apple logo to appear on the screen...but that's it. Cannot reboot it or anything.

Are there any other ways to reboot/restart it...I don't think you can remove the back on these things and take the battery out.

Hold down the power and home button for about 15 seconds, with the charger not plugged into the phone. The Apple logo should come on then possibly go away, if it does try turning the phone on again.

But the apple logo is already on screen...permenantly.

Had already tried plugging it in on charge for a while...no effect. Holding down the power button for any amount of time has no effect at all.

Doing this will do a hard reboot so if it's stuck at the apple logo it should kick it into life

Hold down the power button and home button together, at the same time, for up to 30 seconds.

This. Otherwise it's off to the nearest Apple Store.

Aha...that did the trick. Many thanks!