Hi Bill,
The life of copyright in a photograph is slightly more complicated than you have described. Since you are talking about pictures created during the first half of the twentieth century, it's worth doing a quick summary of the 1911 Copyright Act* which preceeded the current 1988 Act (and the 1956 Act). In that earlier Act copyright existed for a period of 50 years from the end on the year in which the author (ie photographer) died, or if the work had been published, then 50 years from the date of publication. It was possible under the 1911 Act for someone else to obtain a compulsory licence to use the copyright work, 25 years after the death of the author. (If I can find out a bit more about that last provision, I will publish it tomorrow.)
(The 1988 Act increased this period after the death of the author to 70 years for works created after 1989 (with a couple of exceptions) and did away with the distinction between published and unpublished works, at least as far as photographs were concerned - however that's not relevant here).
Fortunately you know the dates of your photographs, even if you don't know the authors. As you have described them as family photographs, I'll assume they haven't been published (I won't go into the technical detail about what constitutes publication now). So in that case, the term is based on the year of death of the author. Realistically with any pictures from around 1925 onwards, the author could still be alive. And for any author who you are fairly certain is dead, they would have needed to have died before 1960 for thier pictures to be out of copyright.
You also mention about taking reasonable steps to track down the copyright owners. Unfortunately the 1988 Act applies here.
Edit: See my second reply below for the correct details
s.57 of the Act describes the level of dilligence need to establish that an author is unknown.
57 Anonymous or pseudonymous works: acts permitted on assumptions as to expiry of copyright or death of author.
(1) Copyright in a literary, dramatic, musical or artistic work is not infringed by an act done at a time when, or in pursuance of arrangements made at a time when—
(a) it is not possible by reasonable inquiry to ascertain the identity of the author, and
(b) it is reasonable to assume—
(i) that copyright has expired, or
(ii) that the author died 70 years or more before the beginning of the calendar year in which the act is done or the arrangements are made.
All of that is what the law says. But here we are talking about family memorabilia, so I think a degree of common sense can be applied. If you have a rough idea who might have taken the photograph, or who is in it, and their heirs are contactable, try and get their agreement for your project; afterall they are the people most likely to object. You don't say how you intend to publish these photographs. If it is on the web, then put a small notice on the site to the effect that if anyone owns the copyright and wishes to object to their use, they should contact you and you will immediately remove the picture in question. If you're publishing in print, this could also apply but obviously you can't recall printed copies as easily as a website can be updated. By following those steps I think you would be showing good faith and shouldn't run into any major problems.
* The terms of 1911 Act were applied retrospectively to photographs etc made before 1911.