Time Machine backup to BT Cloud

lleyamfromlondon wrote:

I was hoping that there was some "hack" that would let me do something like, either mount my cloud storage as a drive and trick Time Machine into using it as target backup location ...

As I wrote the answer to that question is no. Attempts to "hack" or "trick" Time Machine into using a backup device not explicitly enumerated in Apple's Support documentation always fail, with 100% assurance. That doesn't stop people from trying, which is perfectly ok as long as you are prepared to lose that backup.

Given the purpose of a backup, proposing an implementation that is guaranteed to fail seems pointless to me.

... or routinely ship the sparsebundle file on the Time Capsule to my cloud storage.

That's another story. Of course you would need to investigate the feasibility of actually using that sparse bundle disk image to restore a Mac. It would require a multiple step procedure of copying it to an approved device, mounting it, and finally using it, all with a Mac that's not working. At a minimum you would need another Mac to accomplish that task.

lleyamfromlondon wrote:

I have a 1TB of free storage with BT Cloud and I'd like to use it to make an offsite Time Machine backup of my MacBook Pro.

Time Machine does not work with "cloud" storage products or services. To learn how to use Time Machine please read Back up your files with Time Machine on Mac.

You're welcome. Good luck!