I’ve done some checking on Haining’s book, with some interesting results…
Haining has published three separate accounts about Sweeney Todd: The mystery and horrible murders of Sweeney Todd, The Demon Barber of Fleet Street (Frederick Muller Limited, London, 1979); an introduction to a reprint of Frederick Hazleton’s 1862 novel, Sweeney Todd, The Demon Barber of Fleet Street (W. H. Allen, London, 1980) and Sweeney Todd: The Real Story of the Demon Barber of Fleet Street (Boxtree Limited, London, 1993). The OP referred to a subsequent edition of the last of these.
The first of the books is a fairly conventional account. It accepts that the story first appeared in print in The String of Pearls in 1846 (1979, pp. 32-72). It also recognises that parts of the story may have been influenced by earlier stories, whether real or fictional, including that of Sawney Bean, and much space is devoted to the theory that the whole story was originally French (1979, pp. 89-96). On the face of it, the only substantially new material it produces seems to be two reports from the Annual Register, dated December 1784 and April 1785, about murder cases involving unidentified barbers (1979, pp. 120-1). It has to be said that much of the time Haining’s analysis is rather naive. He is too willing to push the evidence so that it fits with his assumption that Sweeney Todd was a real person.
The Hazleton novel was reprinted in 1980 to coincide with the London premiere of the Sondheim musical. Haining’s introduction adds nothing to his earlier arguments.
The real trouble begins with Haining’s 1993 book. Much of this does no more than recycle material from the 1979 book. The big difference however is that, instead of speculating that Todd may have existed, Haining is now able to give detailed information about the real Todd. According to him, the case was widely reported at the time but that it was then forgotten about until Prest retold the story in The String of Pearls over forty years later (1993, p. 110). Let’s examine some of the details.
The magistrate who investigated the case was Sir Richard Blunt (1993, p. 81ff). In naming Blunt as the magistrate, Haining is following some of the late nineteenth century versions of the story. But did he exist? The odd thing about this is that in 1979 Haining had pointed out that ‘Students of the story may be interested to know that Sir Richard Brown was the original name Prest gave to the magistrate. In later editions it becomes Sir Richard Blunt, and this may have something to do with the fact that there was a magistrate, Sir R. Brown, in London in the 1840s’ (1979, p. 60). The index to the 1979 book lists Blunt as a ‘fictional character’. Having checked the standard reference works on baronets and knight, I can say with some certainty that there was no one called either Sir Richard Blunt (or Blount) or Sir Richard Brown in Britain in the late eighteenth century.
The ‘preacher’ of St. Dunstan’s-in-the-West was Joseph Stillingport (1993, p. 82). Haining relies on a report (for which he gives no date), allegedly from ‘the Courier’, in which it is described how the congregation of St. Dunstan’s began to smell the corpses hidden by Todd. This mentions that Stillingport was the minister. Stillingport does not appear in George Hennessy’s Novum Repertorium Ecclesiasticum Parochiale Londoniense (Swan Sonnenschein & Co., London, 1898) - Joseph Williamson was vicar of St. Dunstan’s from 1764 to 1805 (p. 138) - nor was he a graduate of either Oxford or Cambridge. I would therefore suggest that Stillingport never existed. One must also wonder whether the report in the Courier existed either.
The case was reported in the Newgate Calendar (1993, pp. 93, 96, 100, 105). Haining appears to make much use of these reports and even quotes from them. The problem with this is that in 1979 he had claimed that both he and W. O. G. Loftis had made thorough searches of the Newgate Calendar and that neither of them had found any references to Todd (1979, pp. 113-4). Confirming this negative finding would be time-consuming, but the following sites claim to include all the various publications which have been called ‘the Newgate Calendar’.
http://www.exclassics.org/newgate/ngintro.htm
http://www.law.utexas.edu/lpop/etext/completenewgate.htm
Guess what? Neither has any reports about Todd.
Contemporary reports about Todd were published in the Daily Courant (1993, pp. 57-8, 59, 93). But wait a minute, there was no such paper as the Daily Courant in this period. If there had been, one would expect it to be listed in at least some of the following - Tercentenary Handlist of English & Welsh Newspapers, Magazines & Reviews (The Times, London, 1920); R. S. Crane and F. B. Kaye, A census of British Newspapers and Periodicals 1620-1800 (University of North Carolina Press, Chapel Hill, N. C. 1927); R. T. Milford and D. M. Sutherland, A Catalogue of English Newspapers and Periodicals in the Bodleian Library 1622-1800 (Oxford University Press for the Oxford Bibliographical Society, 1936); William S. Ward, Index and Finding List of Serials Published in the British Isles 1789-1832 (University of Kentucky Press, Lexington, 1953); The Waterloo Directory of English Newspapers and Periodicals 1800-1900 (1st series, North Waterloo Academic Press, 1997). (There had been a newspaper called the Daily Courant, founded in 1702 and famous as the world’s first daily paper, but that had been closed down in 1735.) The really suspicious thing is that a news report which Haining in 1979 claimed had appeared in the 3 April 1785 issue of the Annual Register (1979, p. 121) is said by him in 1993 to have appeared in the 14 April 1785 issue of the Daily Courant (1993, p. 57). A check of the Annual Register reveals that the first of the reports that Haining had printed in 1979 does exist (Annual Register, 2nd edn. xxvii. p. 208), but that this second report does not seem to have appeared there either. What makes this particularly worrying is that the second report would be the much more relevant, as it allegedly tells of a murder by an unidentified barber in the street just outside the shop which is traditionally said to have been owned by Todd. In other words, Haining has given two completely different references for this story and both have turned out to be false.
This is enough. What we have suggests that at least some of the sources for which Haining gives a reference, however imprecise, are probably invented. Further checking would no doubt turn up further discrepancies. And yet, as Eve pointed out in her OP, most of Haining’s statements are unsupported by any references at all. Stated very simply, nothing Haining says about events that happened before 1846 can be taken on trust.
Call me cynical but it looks to me as if Haining felt the need to rework his original book (which was neither very good nor very exciting), spicing it up in order to cash in on the success of the Sondheim musical. Its publication in 1993 occured at a time when the musical was about to be revived and when there was, apparently, talk that it would be turned into a film by Tim Burton (1993, p. 147). Even in 1979 Haining may have been inventing evidence but this is nothing compared to the 1993 follow-up, which is completely unreliable and probably downright dishonest. Haining is still claiming that it is a work of non-fiction.
http://www.crimetime.co.uk/interviews/peterhaining.html