"Never done it but from friends and what you see on the TV I don't think the physical aspect of the training should tax anyone that really enjoys pushing themselves"
ho ho ho! sure they were on about The Commando Course at Lympstone? That course will tax ANYONE in the world, regardless of fitness! ;)
Matthew, my own service is the Army so my advice is: don't join the Royals ;) Seriously, you need to be increasing the miles gradually - and you need to be doing speedwork as well; military runs are NOT usually at an easy pace!
Apart from straight road running, try to do cross-country running as well, ideally with some weight on your back. This will pay dividends when the time comes to take on the hard marches that RM training has to offer.
You also need endurance, of all sorts - after doing the assault course on selection you will be ran back to camp as a squad; this is about 5 miles as far as I recall, but you will be knackered already from the assault course so need to have your cardio-vascular fitness up to scratch.
In fitness other than running, I suggest you concentrate on lower weights but more reps, to build endurance; obvioudly don't have the weights too low, and keep them increasing as you get fitter, to push yourself. The goal is to be physically capable and strong, but not to end up as one of those massive blokes that can't hold their rifle in the shoulder more than 3 seconds cos their strength is all in the big, quick lifts.
Last thing of all, good luck! Are you going for selection as a Marine, or are you doing POC? (Several of my mates have done POC)