Hi Rob,
I was in a similar situation a few years ago with some family constraints so you have my sympathies.
The timing does make it difficult as most club and social rides are going to set off a bit earlier, even in high summer. There are a few forumers around your way that I'm aware of, but I'm probably just a bit too far away in Winchester for an 8pm kick-off. If Cyclechat can't help, it might be worth getting in touch with either the Southampton or Winchester CTC groups (both active from what I know) to see if they know anyone around Romsey that needs a late evening ride partner. Sotonia CC (Southampton) and VC Venta (Winch) are your two local road clubs and they might also have some night owls, although expect the standard to be high.
As 'kill says, Romsey's a great kicking off spot for riding as you can head south into the NF (best avoided in high summer), west to the Wellows and Salisbury or north to Stockbridge, Andover and hills beyond, all without touching a busy road.