The book you probably want is "Karst and Caves of Great Britain"
Unfortunately it was quite a small print run, is long out of print and very collectable, so quite expensive if you can find a copy for sale (second hand).
You can read I believe the first chapter online at the JNCC (Joint Nature Conservation Committee) web site.
http://jncc.defra.gov.uk/page-3014
I recall there was an Image bank, somewhere online where all the images from the book could be found, and I also think I found somewhere that had all the text, however I don't recall where.
As it is out of print I would hope the JNCC would make a complete PDF available as they have with some of their other publications but unfortunately I don't believe the have yet.
Somebody on here might know different, or where I may have seen the text or the image bank.
Otherwise, there are regional publications, again mostly out of print, but much easier to come by, but they only really deal with the major Carboniferous Limestone regions. As most of the karst in the UK with significant cave development is of Carboniferous age, the other karst areas don't seem to have attracted the attention of the book writers.
There are plenty of papers and also the regional Geologic Memoirs from the BGS are worthy of a read but they are general geology books rather than a specific treatise on karst...
EDIT:
A quick search of the internet suggests that there are copies available on Amazon.com for $58 which seems a good price to me.
https://www.amazon.com/Karst-Britain-Geological-Conservation-Review/dp/0412788608
FURTHER EDIT:
I found the Image Bank...
http://www.thegcr.org.uk/ImageBank.cfm?v=12&Style=All