Hi Gazz, welcome to the forum.
If your colony swarmed on 30th June, let's assume that there was a just sealed queencell at that time. She would have emerged 8 days later, say 8th July and would need, say 5 or 6 days before she was mature enough to mate, so possibly she would be able to fly from about 14th July. [If you did not cut down queencells to one and left them to it, then a later queen could be present (by a few days)]. If the weather has been good in your parts since then, I would expect that she would be laying from around now as it takes 2 or more days after mating for her to start to lay. In a full colony it takes longer for her to start. As she matures after laying the bees will start to make a space for her to lay eggs in; I would not be worried that she has some restricted space as they WILL want her to lay. However you could take the opportunity to harvest some honey in some form of crush and strain method and put in a couple of frames of foundation to give the bees some space. Or take the queen excluder off for a few days until they start to draw comb in the super. The risk of this is that the queen , if present, may start to lay up there if you leave the excluder off for too long.
May your bees read the same books as you do.