Definitely a Raleigh BSA, so parts easy! Look for Raleighs with full chain cases, and you can complete the 2 missing parts of the chaincase. Hard to find separately.

You need the right cable to get the rear brake going - this guy is helpful and will probably have the cables - http://www.oldbiketrader.co.uk/

Don't strip the hub, but oil it, connect brake cable, and it may all work fine.

please don't repaint the frame - it will look great cleaned up with its patina retained!

That front wheel looks like a 27" ten-speed wheel - You may need to hunt down another "Westrick"-rimmed wheel.

This link sells parts (new) that SHOULD fit the bike, but may be safer to go for original Raleigh bits - http://www.smitexports.com/bicycles.htm

good luck, and keep us posted with progress