I have tried to download four apps on my phone (waitrose was one of them and Next another) and I get is a nondescript icon saying 'waiting'
This has been like that for over a week now
Did you have a good internet connection when you tried to download them?
Try going back to the App store and buying the same apps again (one at a time). It will tell you that it has already been purchased and might kickstart the download again.
You could also try connecting it to iTunes through your computer and select the option to update all apps.