I don’t think you should be worried Steff. I am planning to go on holiday end of June and I am not too worried. My passport was delivered signed for on 14th and Documents Received happened on 24th. I am expecting Application Approved to be early next week and by end of week I expect to have my passport. This is all based on many other experiences I have read so I don’t think what I’m saying is even optimistic. If you’re going holiday in August you have nothing to worry about.
Worst case scenario, you call them up, say someone in your family is ill and you have to visit them and they will give you option to upgrade to 1 day premium or 1 week fast track service. I personally would not recommend as I have seen that these applications are usually done within 1 week from Documents Received stage anyway, so no point wasting your money.
If you can’t get through by phone, just keep pressing # on your dial pad and the operator will get confused and eventually divert you to an actual human being to talk to.