The popularity of collecting rare books is growing. Rare British books in particular remain highly sought after by bibliophiles, or book collectors. Those with a lot of money to spend may collect very old and very scarce "trophy" books such as historically important publications (for example, early William Caxton printed works - William Caxton was the first printer to produce English books using a printing press and also sold books from a shop in the 15th Century). Serious scholars often seek out rare and precious books which contain academic writings. Other book lovers are happy to peruse a library copy.
An increasing number of book collectors are seeking out the books that they enjoyed as children, but, of course, they want the original first editions in excellent condition and with their original dust jackets. Books in this sort of condition tend to survive only in collections because if they were allowed to be read by the average child, their condition would deteriorate very rapidly! Most first edition books (which would usually have been published in hardcover editions prior to the 1930's) tend to be highly sought after and have some value as long as they are in good clean condition. An inscription in a book can add value if it was written by the author (as per the JK Rowling example) or it can detract from the value if it is irrelevant and of no interest to others.
Paperbacks were introducted in to the UK in the 1930s and became immediately popular. Penguin was the largest publisher of paperback books and first editions are also sought after. Because paperbacks were easily torn and damaged, pristine copies with tightly bound pages can be very desirable for collectors, and as Penguin introduced many people to contemporary writers, some of which were fairly controversial at the time, Penguin paperbacks retain a real nostalgia and character than makes them popular to this day.
Apparently collecting rare books has never been so popular so you might want to check your shelves before throwing any books away or donating them for charity just in case you have a hidden treasure.