Several good posts above with info, but I'll chip in too;

Rotrax are one of those brands that are still a little bit unknown even in the UK, knowledgeable people do know about them of course, but they're certainly not one of the first that spring to mind when you ask people to name a bunch English Lightweight builders. In some ways they're becoming less well known, like many of the smaller regional builders, as time goes on and the number of people with 'living memory' of them fades.
The bigger brands that were more prevalent nationwide have a wider following, but a lot of the smaller builders had more localised followings and Rotrax is one such brand.

Like many other builders from the era they built a lot of very good quality 'club' frames, nothing overly fancy, just good quality, well put together and overall quality frames for various uses. They also built some more lavish and fancy 'showcase' frames at the higher end, not necessarily any better riding or especially 'better', but definitely fancier with more elaborate lugwork etc. so you will find examples of both out there.

I actually own 3, despite them being from well before my time, but I have a bit of a thing for seeking out smaller builders and love learning about the history.

One is an unknown model/custom job from the late 40s, I've yet to build it as it needs some repair work as the back end is out of alignment but I'm hoping to get it back on the road at some point.

I've also a couple of 'Shirley' models, one is a 1955 Shirley which has had a repaint at some point but is otherwise unmolested and still has all it's original frame details and is currently built with a Sturmey Archer 3sp AW hub as a classic clubmans bike.

Another is a later (58 I think) Shirley which was significantly renovated about 10 years ago with the addition of downtube shifter mounts, repaced to 130mm, and had a new brake bridge fitted, relocated for 700c and recessed brakes, the fork crown was also drilled at the same time.
This one I have built up with a mix of older and modern parts and I use it as one of my Audax bikes.

It's supremely comfortable due to the long wheelbase (long stays) and very springy fork and jsut eats the miles up, but is still pretty fast. I love riding it and it always brings a smile to my face :-)

Gratuitous pic of one of the Shirley's:


Renovated 50's Rotrax Shirley