Rest will undoubtedly help, Shazza - if you do nothing for a couple of months your legs will get better. But you'll also lose a big chunk of your muscle strength and cardiovascular fitness, and that's presumably not on your agenda.
A physiotherapist should be your first port of call. Ask your GP for an NHS referral - explain that you're a runner, that you need to be fit for...(name a specific race - a 10K in January, the Bath half-marathon in March, the London Marathon) and you will need professional help to keep your other muscles in working order while you rest your calves. If that draws a blank, look in the business directory, or ask around, for a sports physio.
Have your gait analysed and, if necessary, corrected - this may mean a different style of running shoe or a set of orthotics. The Salford option looks a good one for this.
Get stuck into back, hamstring, and gluteal stretches, and make calf stretches part of your routine too once the injuries have healed.
Finally, keeping fit while your legs recover...swimming and other exercises in water are the least likely to aggravate the injury, and indoor rowing (or even normal rowing) should be fine. The stair-climbing machine and the elliptical cross trainer, alas, are best avoided at the moment as unless you've got a spot-on technique they stress your achilles tendon at least as much as running does. Better to have a good walk! The bike (real or stationary) should be fine. Upper body weights, and using the machines rather than free weights for your legs, are OK too.
Keep us up to date with your progress! Achilles tendon injuries are a pain, but they needn't end your running days.