Thankfully, the UK visa system is much less painful than the US system! Visas take around 1-2 weeks to process by post, or same day in person. I had my passport with student visa in my hand eight days after sending the application off via overnight mail.
I applied for my student visa in early August, but that's because I didn't have a choice- I didn't have all of my letters from loan companies until August 1st. I left for the UK on September 8th (I booked my flights before I applied for the visa, in June. Not especially recommended as that's a bit of a gamble, but I really didn't have the funds to pay last-minute prices on a plane ticket.)
If you want to leave in August, then you can apply in May....the official guidelines do state you can only arrive up to one month in advance, but in practice (based on anecdotal evidence from this forum) the consulates in the US don't necessarily stick to that rule 100%. But if you want to be sure, applying in late May for a late August departure should be just fine, as long as all your evidence is in order.