In the old days, this was true. But nowadays that it can take months to get the paperwork through Crapita, the best advice is to apply online ASAP and get the ball rolling. It could be months before you get to the assessment centre anyway, plenty of time to work on your phys.I would sort this out first. If you can't run fast enough or are too fat they won't take you. The required standards for the various roles are all on the Army website. As they're minimum standards my advice would be to get yourself to that level first then apply.
On the subject of older recruits mentioned by others: also nowadays, there are plenty of 30- and 40-somethings who are much, much fitter than the average 20-something. Society is changing and a desperately under-manned Army has to change with it. The Army would do well to focus some advertising on this demographic, I'll bet it would be very successful.