Wardy, wanted to thank you again for the various contributions. Aside from the cycling which I've ramped up again in anticipation of the 100 miler in August, I've made a start on the 5x5 as well; a fairly feeble one (I'm about 175cm / 80kg), but a start nonetheless - 70kg squats, 28kg bench press (had to use dumb bells, no benches were free), 40kg rows. It really doesn't feel like a massive effort at the time, but I do feel it afterwards.
First and foremost, the diet! By that I don't mean only eat rice cakes and drink green smoothies - but you do need to watch what you eat to some degree. Use one of the many free websites/apps that give you a rough idea of your calorie intake. The ballpark figure for men is no more than 2400 per day, obviously depending on your metabolism, body, activity levels etc. If you're well above that, you will need to cut down; there's almost no reasonable way of losing weight unless you have a calorie deficit.
Running will work, but so will many other exercises - cycling, normal gym use, etc. You should notice a more rapid weight loss / muscle and strength gain at the beginning than you would after a few months. Do you have a gym membership somewhere, or would you consider one?