Not sure if the website is broken, but attempting to book 2 people and clicking a time does nothing on iOS Safari. It might be worth looking at the analytics for device distribution but I presume iOS is the bulk of your traffic, si probably worth optimising it.
I noticed this too. I think it’s because those time slots are not available (if you choose a date a couple months away, you’ll be able to click there time slot). The solution would be to print “No availability” instead of disabled time slot buttons.
