All of the very sound advice in these forums has been to reserve your Western Wall Tunnels tour in advance. Though the process usually takes about 5 days, it generally works fine and is so simple even I could do it.
During my visit this May I did notice a couple people without reservations walk up to the ticket window and manage to get tickets for the tour the same day. I definitely wouldn’t recommend showing up and expecting to be able to do this, but I mention it because if you forget or are just unable to book in advance, it can’t hurt to walk up to the ticket window and try to get tickets for that day or the next.
When I was there last month, I walked up and got an English tour 2 hours later.
The closer you get to summer the harder it will be to get walk up tickets. These are not set aside, but are no shows--or people who had the courtesy to call and cancel. BTW I do not know when you are coming, but August is busier than July.
There is always a chance you will be lucky and can get tickets on the spot, but fon't count on it. The odds are stacked against you.
If you are prepared to go there and book a tour for a weird time that day or the next it may work. I once got a booking for 11:30pm. Otherwise if you can prove that your a bride or groom on your wedding day, then they'll let you in immediately!
I have been able to get the 7:00am tickets for the next day, and the 10:30pm and later tickets on the same day. Not everyone's first choice for the timing of the tours so easier to get but still not guaranteed you will get anything that day.