Remember to factor in your refuelling stops. I did just under 100 miles in a moving time of 7:33. But it took me 9 hours because I was tired, (It was my last day of LEJOG and I had ridden the previous 12 days) it was windy and cold. So you will probably need to hit an average of 14.5 for 7 hours with an hour break. I am a little bit older that you but maybe a little bit fitter so I would say that you could do it. As others have said you need to get the miles into your legs. Another couple of bits of advice I have received is
a) Try to do a sportive or two beforehand.
Wiggle offer a few
http://www.ukcyclingevents.co.uk/events/wiggle I am planning for the New Forest and the Ups and Downs.
b) Try and go as fast as you can for as long as you can. 2 hours at a fast pace means you can easily do 4 hours at a slower pace.
c) Get some hill climbing in and repeat these. A lot of the angst about hill climbing is in the mind. Don't try and blast up them but take it at a steady pace.
d) Now that you are into cycling try and get a bike as good as you can. I invested in a carbon frame last year and it is great. I enjoy going out on it.
Finally if you feel that you can't do it come August let me know and I'll take your place. 3 of us applied and only one of us was successful.