You've answered your own question.
You are not running enough weekly mileage to achieve your goals.
You need to build your long run mileage up to 13 and your weekly mileage should be as much as you can achieve without tiring yourself out. The closer to 35 miles a week the better but you may not be able to do this only running 2 or 3 times a week. I would be looking to run 3 or 4X a week.
Your times for the little running that you are doing are quite good, they show that you have potential if you are willing to put the work in.
I wouldn't really worry about speed work at the moment, that's really the icing on the cake. Building your stamina is key here. You need to be able to run the distance with ease.
Sort yourself out with a training plan that you can keep to and fits in with your life. If you have 10 mins to spare then run a mile, if you have to be in then do some exercise that you can do indoors - core for example. If you can get out more then there is no real substitue for running if you want to run.