While I can't really answer your question directly, when doing a bunch of research in months past, the Sigma 120-400mm didn't seem to fare that well in reviews... I suppose 400mm for £600, one has to manage expectations.
Being in a similar situation having Tamron 70-300mm USD (really quite good), though not intending to upgrade for some time, I know that more reach is ALWAYS helpful for wildlife.
But I wonder if 400mm is enough over 300mm? But there aren't many affordable options over 400mm. The only ones I can think of off-hand are the Sigma 150-500mm, Sigma 50-500mm, or the Tamron 20-500mm.
If your current 300mm lens is a good lens, then do a lot of reading on the 120-400mm before considering seriously (assuming you have not done so alread), as I have read that quality drops off after 300mm...