Q. Fresh or aged (well rotted) horse manure?
"bstpierre" A. Well rotted.
Q. Is the soil well cultivated ie Is the horse manure dug at least a spades depth into the ground?
"bstpierre" A. That bed was fairly well mixed to about 18".
Q. Do they get enough water, especially early on & during hot, dry spells in the summer months?
"bstpierre" A. They got plenty of water.
Q. Also during the hot summer months do you mulch them with something like a couple of inches of compost?
"bstpierre" A. No mulch.
Q. Have you tried sowing at 2 week intervals from later April to end of May, just to see if the later sowing works better in your environment (growing conditions)?
"bstpierre" A. I only tried growing them once, but the 2 week interval suggestion would be an interesting experiment.
Then the only couple of things I can think of suggesting at the moment are:
Mulch during the hot summer months, as I've learnt since living here in the US, the heat in the UK doesn't come close to what is experienced over here, therefore mulching tends to be very important, especially during the summer months
Go with the 2 week interval sowing experiment. I think you might discover the shorter growing season works better for your growing environment.
And to answer the original questions:
Q. Why were my parsnips fat?
A. I believe it's most likely a combination of too much fertiliser (soil might be too fertile), too much water (causing some swelling to occur) and being left in the ground too long.
Too much water (during the summer months) = More than, "Water thoroughly once a week in periods of extended dry weather to keep growth from slowing in summer", via University of Illinois Extension. Sorry, could find similar information on the University of New Hamsphire Cooperative Extension site or neighbouring state Extension Office sites.
Q. Why do my parsnips have a woody core?
A. I believe it's most likely caused by them being left in the ground too long, try shortening your growing season by sowing later or experiment by sowing at 2 week intervals to see what works best for your growing environment.