How to improve a HM time???

I am currently training for the Great North Run in September, my first HM race, and am wondering if it is possible for me to stick any chance of beating my cousins too?

Today I have for the first time covered 13.13 miles so now feeling confident that I can cover the distance, I did it in 2:27:48 so not the quickest by any means.

I train 3 x per week and seem to have an issue with pace.  I seem to run my LSR at about half way between tempo and LR pace.  Speed workouts just don't seem to work so good as I tend to give myself asthma attacks

Ideally I don't want to increase my training from 3 days as I have found this is keeping injury at bay, last year suffered achilles tendonitis and a hip issue

For the GNR I'd love to be able to pull a sub 2 hour out the bag, all advice wanted and welcome

You still have plenty of time before the race so Id advise trying to build a good aerobic/endurance base before you start thing about speed. Increasing mileage will allow you body to make adaptations enabling you to feel more comfortable with the distance. As you slowly build your mileage injury is less likely to occur and you'll probably find that increasing the number of times you train per week will be less of a concern. As you get into July and August you can then start to include some speed work into your training. Ensure your diet is well balanced and you get plenty of sleep and just remember to enjoy it.

Thanks for the advice Asics, I was looking to build speed in next month, but think will hold off until July and stay happy with how I am for now.  I'm looking to build to around 15 miles so that I know I can comfortably cover the distance and am looking to build in some of my shorter runs with some hill training in them.  Did a hilly run at my parents couple months ago and it was great, my legs felt so strong as a result.

Building in an extra training day may be difficult with my day job taking up such long hours and my part time job/hobby as a scuba diving instructor and technical diver, but will see if can fit in even a short run