Rivett lathes were the "Creme da la Creme" in the 1920's, not very practical today. You need a lot of gears to cut threads as no gear box. looking at the ways, it has not been cared for. I've only seen one and it was in a museum with an oak cabinet under it.
Difficult to tell exactly which model Rivett although it's an early one. Note the simplicity of the compound dials.
Have you checked tony lathes UK site and compared images?
Here's the page for the #4 which is similar to yours: http://www.lathes.co.uk/rivett34/page2.html
Did you buy that lathe, or were you thinking of buying it? Rivett's are kind of rare and were well made, so you see people asking pretty high prices for them at times. It's difficult to give a solid answer regarding price because they don't come up often enough. I might be wrong, but my sense of the Rivett market is that there a small number of Rivett fanatics out there that all think they're worth a fortune. Personally, I wouldn't pay more than few hundred for it, but that's just me.
Do you want a fully functional lathe to make parts on, or are you more interested because it's a cool old lathe?
I’d like to have it, but it’s not worth anything to me. It would be nice to see in person. If I could get it for a couple hundred at auction, I’d try for it. Anything over what you paid is a profit. Ask more than you think it’s worth. You can always deal down. One way to check is by going to EBay and auditing “completed listings”. This will show you the things that actually sold, instead of just what people are asking. Gives a good idea what the value is to buyers.