Parsnips are sensitive, maybe more so than other root vegetables, to the PH level of your soil. Here, in the western U.S., we add lime each spring to help. You might want to do a quick soil sample test. The soil should be as close to neutral as you can get... 6.5 at least.
You do know that they take a long time to grow, no? Don't be in a rush to harvest this fall... inf act their quality dramtaically improves if they aren't harvest until after a light frost or two.
As soon as they're up and running thin them to about 6 inches and you'll find they produce a better crop.
Best of luck!