I just sold an Raleigh Sports ladies model here in fair condition for $200, it seems old English three speeds have a real following. There's a few listed on CL here for well over $200, and a few that were over $400 that went up, and came right down after only a few days.
Older the better seems to be the ticket, they made those bikes from the 30's up to the 80's.
The crank you have is earlier, they dropped some of the braces around the chain ring in the later models, and I think reflectors on pedals started in 1969 on those. Somewhere in the 1950's they changed to a 46t chainring too, yours looks like a 48 or 50t version. My guess is that those are 50's cranks. If the chrome is decent and the chain ring is good I'd list them on fleabay at around $40. The bottom bracket in those bikes is also all its own, with 28tpi threads and 72mm wide. The cups and crank axle, if they're still good, are also worth listing. So are early hubs, the Sturmey Archer rear hubs are dated with the month and year.
Early shifters are also hard to find in good shape. Any version without plastic is a decent find.
The general consensus is that the bike built prior to Raleigh being bought out by Tube Industries in 1960 were better bikes. Earlier frames have an oil port on the BB shell and most retain the boss for attaching an enclosed chaincase on the right chainstay just behind the BB shell.