I think my internal wi-fi (see make and model etc in my signature) might be breaking down.Is there a way I can test it?

There's no wi-fi information in the signature. Which channel are you using and which mode? Without any information, my first guess would be to check with kismet or similar for interference on the same or, more likely, adjacent channels. If possible quit the 2.4GHz band and upgrade to the 5GHz band exclusively.

Although you posted the make/model of your laptop it could be either an Intel or Broadcom wireless chipset installed.

What symptoms are you experiencing that you think your wireless is breaking down?

There are many factors that can affect speed i.e transmit power, distance from access point, the stuff between the laptop and the access point, other nearby channels/computers, the access point/router itself and so on.

For an internal LAN test you can use nc or file transfer protocol like scp that will output a transfer rate between a wired computer and your laptop. The transfer rate will be as fast as the slowest connection.