It's a webdesigner who is usually paid before he does the job. But if he (the webdesigner) is too busy, he will tell the client before, so the client would not pay for an undone job. The client will have to wait until the webdesigner has more time.
There is no need to say anything. The clients will find out that the webdesigner cannot take on any more work at present when the webdesigner informs them. There is no question of any payment until both sides have agreed that the work will be done.