Following up on an application

I applied for a job on the 30th of July and haven't heard anything yet, I got a automatic message back saying the usual thanking me for applying and also added "if we don't get back to you straight away don't panic we are probably in the kitchen garden".

What would people class as a striaght away response, Would a follow up email ruin my chances or could I follow up as it's been nearly 3 weeks now?

Any advise would be appreciated.