Many of you were in the right ball park with early 1930's making it one of the last pre-Beck maps, but the correct answer was 1932. Take a look at Clive's site which has most of the variants of London Undeground maps dating back to 1889.
In terms of the current names of the lines in the Edwardian Tube map here - between all of you, you guessed most of them:
Central London Railway is today's Central Line City and South London is part of today's the Northern Line via Bank Great Northern, Piccadilly and Brompton is the Piccadilly Line Great Northern and City is the WAGN line or Northern City (which isn't part of the London Underground any more) Charing Cross, Euston and Hampstead is the Northern Line via Charing Cross Baker Street and Waterloo is the Bakerloo Line and of course the Waterloo & City is now the Waterloo & City Line which was too easy to guess.
BTW 2 - Metro have a fiendishly difficult competition today where you can win a copy of Mr Beck's Underground Map by Ken Garland and Underground Maps after Beck by Max Roberts (who's been commenting on this blog of late). To win you need to answer "How many copies of the London Underground map are distributed each year?" and email your answer with your name and telephone number to email@example.com by 5pm tonight. The answer is on a link somewhere in this post. The winner will be picked at random from all of the correct entries. Good luck!