Hey Fiona,
A light grey background is by no means a bad thing. Sometimes a flat white background will make a product look like it's floating in air, which can look odd.
There is, however, a cool little tutorial on building a really effective lightbox. I know you said you already shoot with one but it's quick to but together and you might find that light levels differ from lightbox to lightbox, depending on your materials, lights used, etc.
https://blog.etsy.com/uk/2014/06/19/how-to-lightbox/You also might want to try fine-tuning the settings on your camera. If the background is coming out too dark then, if you're able to take manual control of your shutter speed, I'd recommend adjusting it.
Unfortunately there is no simple, catch-all solution. There could be a range of factors that aren't giving you satisfactory result. Keep plugging away and keep notes so that its replicate-able when you fine the right settings.
Have fun.
Adam.