Most - probably all - of the books listed here are out of print. I've managed to collect them all, and can recommend them to anyone wanting to delve further into the history of broadcasting (if you can find copies).
THE HISTORY OF BROADCASTING IN THE UNITED KINGDOM
by Asa Briggs (Oxford University Press)
Volume 1: THE BIRTH OF BROADCASTING (1961)
Volume 2: THE GOLDEN AGE OF WIRELESS (1965)
Volume 3: THE WAR OF WORDS (1970)
Volume 4: SOUND AND VISION (1979) ISBN 0-19-212967-8
Volume 5: COMPETITION 1955-1974 (1995) ISBN 0-19-215964-X
The bible of UK broadcasting history to 1974, immensely detailed and meticulously reseached.
A HISTORY OF BROADCASTING IN THE UNITED STATES
by Erik Barnouw
Volume 1: A TOWER IN BABEL - to 1933 (Oxford University Press, New York, 1966)
Volume 2: THE GOLDEN WEB - 1933 to 1953 (Oxford University Press, New York, 1968)
Volume 3: THE IMAGE EMPIRE - from 1953 (Oxford University Press, New York, 1970)
Does for American broadcasting what Briggs did for UK broadcasting: very detailed and authoritative.
TUBE OF PLENTY - THE EVOLUTION OF AMERICAN TELEVISION
by Erik Barnouw (Oxford University Press, New York 1975; revised paperback 1977)
Summarizes the three books above and brings the history up to 1975. A useful condensation.
BRITISH BROADCASTING
compiled and edited by Anthony Smith (David & Charles, 1974) ISBN 0 7153 6326 3
Compilation of articles, papers and other sources on the subject.
BROADCASTING FROM WITHIN
by C. A. Lewis (Newnes, 1924)
Examination of early BBC history and methods by the then Organiser of Programmes.
THE POWER BEHIND THE MICROPHONE
by P.P.Eckersley (The Scientific Book Club, 1941)
A critical examination of the BBC by its first Chief Engineer.
BROADCASTING HOUSE (BBC, 1932)
Detailed look at the then new building, with many photographs and complete floor plans. Roger Beckwith has posted the entire contents on his site.
THE THIRD FLOOR FRONT - A View of Broadcasting in the Sixties
by Sir Hugh Greene (Bodley Head, 1969) ISBN 0 370 01310 7
Greene was the Director-General of the BBC for most of the 1960s.
FACING THE NATION - Television and Politics 1936-1976
by Grace Wyndham Goldie (Bodley Head, 1977) ISBN 0 370 01383 2
A detailed view of the difficult relationship between the BBC and politicians, by an experienced television producer.
A SEAMLESS ROBE - Broadcasting - Philosophy and Practice
by Charles Curran (Collins, 1979) ISBN 0 00 211864 5
Curran was Director-General of the BBC from 1969-1977.
THE LAST DAYS OF THE BEEB
by Michael Leapman (Allen and Unwin, 1986, revised paperback Coronet, 1987, ISBN 0 340 41107 4)
The inside story of the difficult period the BBC went through in the 1980s.
LET TRUTH BE TOLD - 50 Years of BBC External Broadcasting
by Gerard Mansell (Weidenfeld and Nicolson, 1982) ISBN 0 297 78158 8
Mansell was Managing Director of the BBC External Services (now the BBC World Service) from 1971-1980.
HOW TO WRITE BROADCAST PLAYS
by Val Gielgud (Hurst & Blackett; no date given, c.1933)
A short article on the technique of radio drama (in which the author was a major innovator) and three play scripts.
BRITISH RADIO DRAMA
edited by John Drakakis (Cambridge University Press 1981) paperback ISBN 0 521 29383 9
A collection of articles on the history of radio drama.
LOUIS MACNEICE AT THE BBC
by Barbara Coulton (Faber and Faber, 1980) ISBN 0 571 11537 3
The career of one of radio's leading dramatists.
GOODNIGHT CHILDREN... EVERYWHERE - an informal history of children's broadcasting
by Ian Hartley (Midas, 1983) ISBN 0 85936 201 9
Includes Children's Hour, Radio Luxembourg and BBC Television.
A MICROPHONE AND A FREQUENCY - Forty years of Forces Broadcasting
by Doreen Taylor (Heinemann, 1983) ISBN 0 434 75710 1
The history of broadcasting for British Armed Forces overseas.
RADIO - A TRUE LOVE STORY
by Libby Purves (Hodder & Stoughton, 2002; Coronet paperback 2003, ISBN 0 340 82242 2)
A personal account of latter-day radio by my erstwhile colleague as a Studio Manager, later a well-known broadcaster.
DUE TO CIRCUMSTANCES BEYOND OUR CONTROL...
by Fred W. Friendly (Random House, New York, 1967)
The story of CBS news programmes and their leading reporter/commentator Ed Murrow, by his producer.
THE SPONSOR - Notes on a modern potentate
by Erik Barnouw (Oxford University Press, New York, 1978; paperback 1979 ISBN 0 19 502614)
An examination of the relationship between American Broadcasting and the advertisers.
Also various BBC Handbooks/Yearbooks (very rare) starting in 1928.
TECHNICAL HISTORY
BBC ENGINEERING 1922-1972
by Edward Pawley (BBC Publications, 1972)
Technical history, very detailed: the most authoritative source on the subject.
TELEVISION UP-TO-DATE
by R. W. Hutchinson (University Tutorial Press, 1935)
Technical manual, including both the several Baird and the EMI systems.
ENGINEERING DIVISION TRAINING MANUAL (BBC, 1942)
Detailed technical manual for internal use.
MAGNETIC RECORDING
by S. J. Begun (Murray Hill, 1949 - British reprint by Thermionic Products Ltd)
Very detailed manual on the theory and then practice of magnetic recording, both wire and tape.
BBC RECORDING TRAINING MANUAL (BBC, 1950)
Detailed manual including information on disks, Marconi-Stille and Philips-Miller.
SOUND RECORDING AND REPRODUCTION (Iliffe & Sons, 1950)
Revised version of the above for general publication.
HIGH-QUALITY SOUND PRODUCTION AND REPRODUCTION
by H. Burrell Haddon (Iliffe, 1962)
Published version of BBC Training Manual covering all aspects of recording and broadcasting: for many years the standard training reference.