Thank you for everyone's comments. Happily, a plumber who is also a drain specialist came out yesterday and did a fantastic job of clearing the pipes. For the sake of completing this thread, he said the advice about installing a Saniflow or waste disposal to 'jet the water down the pipes' that I'd been given by the previous plumber was not good, nor does he use harsh chemicals such as One Shot which can apparently damage the pipework if it ends up pooling in any area of the pipe. Now that the drain is clear, he advised me to use soda crystals on a regular basis overnight (slow release via a loose plug) to dissolve any fat lingering in the pipes.