Legally, you are pefectly entitled to shoot anywhere on your property provided:
The ammuniion doesn't leave your lawful boundaries (fences and the like normally determine these) unless you also have permission of the land owner where the pellets will pass through and eventually land.
And
You don't cause a public distress.
Example A - shooting in your from garden. Legal but stupid.
You can shoot there, but typically front gardens a visible to the public. If somebody reports you the firearms teams will turn up. You could be prosecuted for causing distress to the public but not for the actual shooting of the gun.
Example B - shooting targets on a fence.
If you line up targets on top of a fence or wall, missed shots could travel past your boundary. This is technically armed trespass unless the neigbours know it is happening and give permission, otherwise it is VERY illegal. If the pellets travel onto public land (the road for example) this is also armed tresapass.
Advice:
Make a flyer detailing your intentions. Explain what the ammo is and that the gun is essentially a radio controlled car in a different body.
Maybe use Google maps to get an aerial photo of your garden and the surrounding area and detail where you plan to shoot
Drop it off to all neighbours who have a window overlooking your garden.
Make sure it have a pellet catcher behind the target. I favour some kind of box opening with loose towels in it to absorb the impact.
Basically you need to do everything you can to not be seen by the public or calm their fears if they see you.
Happy shooting and dont forget your eye protection