I haven't been to Newmarket either but I usually look for either a decent layby or an industrial estate, we stay very regular in industrial estates in the road not on the private land outside the units.
Never had an issue in either and often end up either parking up or waking up next to a sleeping lorry driver.
Just outside Poole in Dorset we stopped in a layby, I use it regularly, when I got up there were another 4 motorhomes all parked behind us!
Rolling on and enjoying life on the road