You intend to remove the bumper and use the car.
Alephzero's answer gives legislation governing the visibility of number plates (basically, vertical and clearly visible).
Your car must not pose an undue danger to other road users. Of course, any car hitting a pedestrian or cyclist is Not A Good Thing, but if the absence of a bumper exposes parts which will cause greater injuries than when the bumper is present, you may fall foul of police or VOSA. Construction & Use Regulation 100(1) is rather widely-drawn. Note also MoT section 6.1.4 — your vehicle will fail an MoT test with the bumper in its current state or removed, and the dangerous state of the vehicle might be an offence under Section 40A of the RTA1988. You ought also to consider your insurance, as using a vehicle in a dangerous condition might invalidate it.
All of that said, perhaps without the bumper there is still somewhere that the existing plate can be fixed temporarily in much the same position as with the bumper. There appears to be some sort of horizontal bar which might suffice.
If that fails, then getting a flexible/self-adhesive "plate" made would mean that it could be stuck to the bonnet between the headlights. You might need to remove the badge, and there's no guarantee that it would come off cleanly (plates aren't supposed to be easily removable). You may feel that's an option which could be retained with a new bumper — perhaps a special aftermarket one which doesn't have provision for the plate.
Fixing a number plate with cable ties or something similar makes it very easy for thieves to take, so they have double the time to spend on removing the rear plate.