I switch my broadband router off every night to conserve energy, but have noticed the broadband speed getting slower, is this normal?

A very common problem I have encountered over the years. Routers are designed to be left on at all times. The line is monitored at the exchange end by what’s called a DLM or Dynamic Line Manager, which is trying to keep and maintain the fastest stable broadband speed possible to your router. If this is switched off on a regular basis, the system assumes this as an unstable line, and will gradually drop your connection speed to try and stabilise the losses in connection (this also happens when you have a crackly or dead telephone line).
Always try to keep your router switched on as much as possible, although the system will ignore the odd loss of connection eg during power cuts, holidays etc., as normal.