The basic rule on copyright material* in the UK is that the period of copyright runs for 70 years from the end of the year in which the author/photographer dies. So realistically all the pictures you are dealing with could
still be in copyright. If the postcards have the name of either the photographer or publisher on them, you at least have something with which to track down the current owner of the copyright - say a relative or heir.
But as I think you have already discovered, things are more complicated than that! Section 12(3) of the Copyright Designs and Patents Act 1988 provides that if the author is unknown, then the period of copyright of 70 years runs from the end of the year that the photograph was created or
was first made available to the public, whichever is the later. Full details can be found here
Where the name of the author is known but it is impossible to find out when he died, the date of making/publication may also be used as the starting point in certain circumstances.
Section 57 of the Copyright, Designs and Patents Act 1988 says that copyright is not infringed if after reasonable inquiry the identiity of the author cannot be found and
it is reasonable to assume that the author died more than 70 years ago. So taking an example of a postcard from 1900, the photographer might have been aged 25 at the time and gone on to live a further 50 years, so died in 1950. That would mean the copyright period has another ten and a half years to run. Is it reasonable to assume that the photographer was 25 at the time? I don't know the answer to that. But certainly for the pictures from the 1940s I don't think it would be reasonable to assume that the author is even dead, let alone that the 70 years period has elapsed.
There is some better news concerning the postcards. Where the date of publication is known, but neither the name of the author, nor the date of his death can be ascertained, Section 104 (5) says that the date of publication can be assumed as the starting point for calculating the copyright period (ie the 70 years). So any postcard from the period 1900-1939 where the name and and date of death of the author cannot be ascertained
is now out of copyright under this rule. Obviously this is not much use if the date of publication is also not known.
You mention that this project is for educational purposes. However, although certain forms of copying of copyright works for educational purposes is permitted, this does not allow the copies to be communicated to the public, which of course is what would apply if these pictures were put on a website. Also you as an individual do not qualify as 'an educational establishment' for the purposes of this exemption.
So, to summarise, assuming that you cannot, after reasonable inquiry, discover the name of the author/photographer, but you can establish the date when the photograph was either taken or published, and this date is before 1940, then the picture is llikely to be out of copyright under the provisions of Section 12(3).
Your final point concerns what rights, if any, other people who have published the photographs can claim. If you have an original postcard or photographic print, then any rights in them are determined just by the various dates discussed above. However if you copy an image from a book of photographs then you may infringe the copyright of the author of the book. So the fact that you may have an original postcard, but that same picture has also been published in a book, does not give the book's author any claim unless he can show that he has an exclusive licence to publish the image. Even if he can show this, the relevant dates for determining the period of the licence are the same as for the copyright in the original image, and not the date of publication of the book etc. In the case of another website, because it is not protected by the typographical layout provisions which apply to a book, the site owner has no special claim to copyright in the image unless he is the author or can show that he has an exclusive licence to use the image.
* The period of copyright for performances, sound recordings and broadcasts etc is 50 years from the first performance, broadcast etc.