It is not illegal to go back yard plinking.
You do however, need to go around all your neighbours and explain what it is that they may hear or see and that its a piece of sports equipment that looks like a rifle.
ALWAYS shoot towards YOUR PROPERTY so that any damage is yours to fix at your leisure.
Your BB's must not have a path to or enter in to the public spaces outside your backyard space as it becomes a big legal issue if you were to hit someone or something and it got damaged ands you were seen,etc, then things get a bit legal.
I wouldn't refer to it as target practice either, that implies something else, plinking is the proper term to use and I'd buy a few plinking toys to target practice with and a few catch boxes to catch your BB's in or you can make one easily, just pack it with old paper and bubble wrap and it be atleast 6 inches thick and the BB's won't go through the box, I use both a cardboard box and a couple of catch boxes for indoor practice.
If you go indoors, wear eye pros because BB's can come back at you with some force.
I'd also arm yourself with a copy of the relevant legislation as you never know, there may be that one or two neighbours that will disagree with you on the law and because they are closed minded and see everything as violence, will report you each time you are out, let them, that can be deemed as harassment to you for going about a hobby you are legally allowed to do on your own property in your back garden (the assumption that its all closed in) but note, if your garden is not enclosed by high fences, you won't be able to do any plinking until you put in higher fencing.