LONDON — Ever since China announced last year that it no longer wanted to be the “world’s garbage dump,” recycling about half of the globe’s plastics and paper products, Western nations have been puzzling over what to do when the ban went into effect, which it did on Jan. 1.

The answer, to date, in Britain at least, is nothing. At least one waste disposal site in London is already seeing a buildup of plastic recyclables and has had to pay to have some of it removed.

Similar backups have been reported in Canada, Ireland, Germany and several other European nations, while tons of rubbish is piling up in port cities like Hong Kong.

Steve Frank, of Pioneer Recycling in Oregon, owns two plants that collect and sort 220,000 tons of recyclable materials each year. A majority of it was until recently exported to China.