Determining first edition?

I'm interested in finding out whether a book I've got is actually a first
edition or not. I mostly wanted it to read, so it doesn't matter that
much, but I might either want to start collecting the rest of the
series to match, or to sell it one day, and it'd be nice to know. I
could find very little information about it online, as it's quite rare
(I've been looking for a reasonable priced copy for ages!).

The book is Words and Music, by William Mayne, the fourth book of his
Cathedral Quartet. The copyright page says "First published in Great
Britain in 1963", and the underneatht there's a copyright 1963 sign.
There no mention of other printings or editions. It's rare enough that I
suspect there were not very many printings, possibly not more than one, or
you'd think it'd be a bit easier to find. So all tha that sounds like it
probably is. However, on the back of the dust jacket, there is a list of
his other books, and the bookseller pointed out that one of them,
Whistling Rufus, was not published until 1964, so he wasn't really sure if
it was a first edition or not. He said that sometimes publishers would
list books that were about to be published, though, so it doesn't
necessarily mean it's not a first edition. The publisher of Words and
Music is Hamish Hamilton; the publisher listed under Whistling Rufus is
Reindeer Books. (Perhaps HH was told that it was going to be published in
'63, but Reindeer Books didn't get round to actually doing it until '64?)

Any ideas how I can find out about it? I tried to find a biography of
William Mayne, but nothing I came across had this level of detail.

I have the first two books of the series is the paperback versions
released in the past 10 years, and I found an old secondhand paperback of
the third, but I have never seen this one, the fourth in the series, in
paperback, so perhaps it was less popoular than the others. I was always
waiting for a paperback to come available second hand, as I thought I
would be more likely to be able to afford it, but one never did. Even
ex-library copies seem scarce, and the only ones I saw were like the one I
bought, probably remaindered and never read (price clipped - does that
mean remaindered?)

thanks for any ideas on how to find out more.