Looking at that image, as Feanor said, wouldn't you just have a large piece of the cycle-hoop left connected to the lock and bike? Arguably that would be theft from the local council, if you removed it (unless it's on a private location, and you have permission).
I looked closely at one of those a few years ago, and that one appeared to just have normal Allen-key fittings, which surprised me, but I'm prepared to accept that better fixings are also used.
Unless it's an exceptional D-Lock, a battery powered angle-grinder seems the obvious approach. My boss removed his D-Lock, when the lock barrel failed, with a lump hammer that he borrowed off of me. However, the lock was next to a convenient wall, which probably isn't the case with the Cycle-Hoop. I've experimented with my small Lidl angle-grinder, and it cut through a fairly random D-Lock in a few minutes.
Borrow an angle-grinder, wear safety goggles, carry ID, and take something to protect the bike from sparks thrown off of the cutting blade (I'd guess an old towel or newspapers would probably do the job). Spare blades and batteries are a good idea, in case you have problems or complexities. Some sort of locking tool, like mole-grips, would also probably be a good idea to hold the lock securely, without getting too close to a rapidly spinning blade!
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