I have a mid-2010 15" MacBook Pro. I have purchased a mini DisplayPort to DVI-D adapter onto which I have connected a DVI-D to VGA (D-Sub) adapter which then connects into my new monitor. The Displays screen seems to recognised the monitor, but the monitor says "No Signal Detected". Is it valid to connect mini DisplayPort -> DVI-D -> VGA?
No. DVI-D only carries digital signals. Most (if not all) DVI -> VGA converters use the analog signal DVI-I carries. A mini DisplayPort to DVI connector will only pass on digital signals (as you correctly identified by referring to it as a DVI-D signal), so your DVI to VGA adapter is left out in the cold. You need to get a mini DisplayPort to VGA adapter.
The reason the computer sees the display is that one of your adapters is identifying itself as a display.