Brynley, you did great. I looked for a Rudge for 30 years before finding mine. It's the only English 3-speed that I like better than the Raleigh. Mine is a 1962 or so, and it doesn't have the cool chainring, so I'm envious.
Raleigh bought most of the English bike companies in 1960, including Rudge, and it continued making Raleighs with various names stamped on them, including Rudge. The Raleigh-made Rudges (such as yours and mine) have some Rudge-specific parts, such as the chainring (not mine) and the fork. I love the look of the fork.
The repairs are likely to be straightforward for you. It's a matter of disassembling, dissolving the grease, which has now turned to glue, regreasing, and reassembling.
Those saddles are still made, and you can get one, used or new. A couple of us on bikeforums are learning the craft of saddle recovering, which involves replacing the entire leather piece. They are very good saddles, and if you take care of them, they last longer than other types. Mine is original, and it has many cracks, but it's not falling apart.
Read about mine earlier on in this thread and also in the thread I started here.