Heraldic designs are subject to copyright in the same way as as other artistic works. Therefore copying them in the way you describe certainly sounds as if it would infringe unless one of the exceptions to copyright might apply. However, using the written description of a grant of arms such as
Per fess Purpure and Or a Pale counterchanged in the Purpure an Asprey Cut Diamond of cushion shape culet downwards Argent and in the Or an Ancient Crown Purpure.
Source: College of Arms Newsletter Sept 2007. Grant of Arms to Asprey Holdings Ltd
to create a new artwork using the artist's imagination and knowledge of the terms used, would not be infringement, as it is somewhat like making a cake from someone else's recipe.
You mention that these are historic designs. If you can reasonably assume due to their age that the original artist died over 70 years ago, then the design should be out of copyright. However if the authors of the book have reproduced the arms in much the same way as your illustrator, the images in the book may attract copyright because they are new works. It would be worth checking to see exactly what the book says about how their illustrations were produced. If they are just photographs of the original arms, then you don't need to worry so much, provided that the original object is out of copyright.
I mentioned exceptions. There are two that may cover what you want to do. They both come under the heading of fair dealing, which means generally speaking, that no more of the original work is used than is necessary, and that the original source must be credited. The first use is for private study or non-commercial research. This may fit your purposes, as long as you make it very clear that the images are only made available for private research purposes. This exception does not cover any intended commercial use. Here's what the law says:
29 Research and private study.
(1) Fair dealing with a literary, dramatic, musical or artistic work for the purposes of research for a non-commercial purpose does not infringe any copyright in the work provided that it is accompanied by a sufficient acknowledgement.
(1B) No acknowledgement is required in connection with fair dealing for the purposes mentioned in subsection (1) where this would be impossible for reasons of practicality or otherwise.
(1C) Fair dealing with a literary, dramatic, musical or artistic work for the purposes of private study does not infringe any copyright in the work.
(2) Fair dealing with the typographical arrangement of a published edition for the purposes of research or private study does not infringe any copyright in the arrangement.
(3) Copying by a person other than the researcher or student himself is not fair dealing ifâ€”
- (a) in the case of a librarian, or a person acting on behalf of a librarian, he does anything which regulations under section 40 would not permit to be done under section 38 or 39 (articles or parts of published works: restriction on multiple copies of same material), or
(b) in any other case, the person doing the copying knows or has reason to believe that it will result in copies of substantially the same material being provided to more than one person at substantially the same time and for substantially the same purpose.
(4) It is not fair dealingâ€”
- (a) to convert a computer program expressed in a low level language into a version expressed in a higher level language, or
(b) incidentally in the course of so converting the program, to copy it,
(these acts being permitted if done in accordance with section 50B (decompilation)).
(4A) It is not fair dealing to observe, study or test the functioning of a computer program in order to determine the ideas and principles which underlie any element of the program (these acts being permitted if done in accordance with section 50BA (observing, studying and testing)).
The second fair dealing category is for the purposes of quotation. This exception does allow commercial use. However if you rely on this exception (as I do for the description of the grant shown in my first paragraph), then you should still make sure that you credit the original source.
(1ZA) Copyright in a work is not infringed by the use of a quotation from the work (whether for criticism or review or otherwise) provided thatâ€”
- (a) the work has been made available to the public,
(b) the use of the quotation is fair dealing with the work,
(c) the extent of the quotation is no more than is required by the specific purpose for which it is used, and
(d) the quotation is accompanied by a sufficient acknowledgement (unless this would be impossible for reasons of practicality or otherwise)
Alternatively your could contact the publisher of the book and seek permission to use the illustrations you need. Better still seek out the source that the book's author has used and, if that is out of copyright due to its age, you can freely copy it without worrying about the book.
Finally, a word of caution about how the arms are used by visitors to your website. It is technically illegal to 'bear' arms etc which have not been awarded to that individual. So a child who paints a real coat of arms on a shield for use in a school play or pageant would technically be committing an offence and could be hauled up before the Court of Chivalry
! Since you aim to teach about heraldry, it might be worth pointing this out.