That depends: https://en.wikipedia.org/wiki/Public_Lending_Right

"A Public Lending Right (PLR) programme, is a programme intended to either compensate authors for the potential loss of sales from their works being available in public libraries [...] Canada, the United Kingdom, all the Scandinavian countries, Germany, Austria, Belgium, the Netherlands, Israel, Australia, and New Zealand currently have PLR programmes. [...] How amounts of payment are determined also varies from country to country. Some pay based on how many times a book has been taken out of a library, others use a simpler system of payment based simply on whether a library owns a book or not. [...] In the United Kingdom authors are paid on a per-loan basis calculated from a representative sample of libraries. The current rate is 7.82 pence per individual loan."

(I imagine that any occurrences of "authors are paid" should be replaced by "publishers are paid", but I don't know specifics.)