Is 17 miles (27km) each way a lot for a newbie cyclist? I go to the gym on a regular basis and do a fair bit of running. I feel like I'm fit enough to do this. It would be a one-off ride from Wembley to Slough and back so it would be a fair bit of road which could be a problem.
As a one-off, that should be completely doable. Your fitness from running and the gym should be plenty enough, especially as the route is pretty flat. Bear in mind that it will be tiring, since cycling uses different muscles to running, and the saddle may get a bit uncomfortable if you're not used to it.  Make sure you have plenty of water and something like a cereal bar or a banana to eat half-way would be good, too. (You want something that will release energy over time, rather than a big sugar hit.)

Riding in traffic can be mentally tiring when you're not used to it so definitely consider a route using quieter roads and cycle paths, even if that adds a few miles. The thing you want to avoid most is narrow roads with lots of traffic: if cars can overtake you easily, everybody's much happier.

And there's lots of public transport available so, if you get to Slough and can't bear the thought of cycling home again, you can always get on a train, though don't try to do that at rush-hour.