Can you get in legal trouble for growing 1 weed plant in the UK?

No, it is not legal to grow even 1 weed plant in the UK. While the chance of cops finding out is less, considering it is illegal, it wouldn't be a good idea. Your neighbour might tell cops. If you get caught, then it could lead to harsh punishment. You might get a hefty fine and even get sentenced to a couple of months or years.