I don't know which RHS course you're starting with, so the ones I'm recommending may be too advanced for what you're doing, but two books you could obtain, and if you're dedicated, read and learn from:-
Botany: an Introduction to Plant Biology ISBN 0-471-86840-X
The Nature and Properties of Soils ISBN 0-02-313371-6
Both these were recommended resource materials when I did my RHS M Hort some years ago, and are still available. They are both large, relatively expensive and heavy textbooks.
An extra little one that you might find useful is:-
Plant Names Simplified: Their Pronunciation, Derivation and Meaning by A.T. Johnson and H. A Smith - this one now appears to be available on Amazon for £7.25, so pretty inexpensive. I can't find my own copy to give you the ISBN number, but it seems to be readily available. It's a useful little book, not least because it explains or translates the Latin terminology of parts of plant names.
The Longman Botany Handbook might be of some use, though its primarily aimed at advanced A level students (those in Sixth Form college or similar), but it does contain some useful, basic stuff. It's a sort of dictionary format, might be useful to you, not expensive to buy - ISBN 0-582-09965-X.
The RHS produces its own Gardener's Encylopaedia of Plants and Flowers, but if you choose to buy any publication listing plants, make sure it's a recent edition of whatever it is, or that it's been updated some time in the last 5 years. DNA research has meant many plants have been renamed and reclassified in recent years.