If you ride fast enough your body will generate enough heat to keep you relatively warm. But a lightweight vented wind/waterproof over your appropriate clothing imho is a worthwile addition. Aldi are selling them in a couple of weeks, they were only about a tenner last year and fit well in the backpocket of a jersey. Also decent overshoes as your feet are the hardest part of your body to keep warm.
The other thing I would recommend in the rain is mudguards if you can fit them on your bike. It is much nicer cycling in the rain with mudguards both for you and those around you.