Hi Jo
You can DEFINITELY do the 10k - if I can - you certainly can...!! I'm the same as you in that I started running early this year (and, not the same as you, 3 1/2 stones overweight). I did my 1st the 5k Race for life in May (42 mins) and (at the time, stupidly) entered the Jubilee 10k a week later (to keep me running)!!
I also felt I wasn't improving and was running about 30mins 1x per week on a treadmill and 30-40mins 1x per week outside. But, as V-rap advises, cross training really helps and I started cycling to work. I also built up my runs, increasing them by 5/10 mins each week until I could run (v. slowly, for 1hr 10mins) 2 weeks before the 10k)...Consequently, my endurance has
really improved, but I'm sill very slow. I've since lost over 2 stones, and the 10k was 3 wks ago, but it still took me 77 mins to complete (and that was with no stopping or walking!).
To get faster I'm following Susies advice from this forum and I've just started doing fartleks on the treadmill (only 2 sessions so far) and on my run tonight I took 2 mins off the 5k route normally do (usually takes me 38 mins), so I'm really chuffed with that. Maybe you could try that when you're at the gym?
I really hope you do it Jo. Don't be discouraged by others that may be faster than you - you will get faster, but it does take time. 10k it's really not as terrifying as it sounds and as I thought it would be when I was at the start line.. It was the best experience I've had this year and I'm planning to do a 1/2 marathon next! If you think to yourself that it's really not important how long it takes, you really do take the pressure of yourself and just enjoy it. Concentrate on being able to run for longer periods of time and build up your stamina and you'll be fine!
Kate