CC sites are notoriously difficult to book into unless you plan your trips the previous December.
We are just up the road in Sheffield and have family in Ilkestone.
As you are in Nottingham why not have look around NE Lincs and stay on of the many CL's. Most do have hook up, some a shower( although basic) and they usually have a loo. They are very quiet and often have room for kids to run around
( but beware , on many sites dogs seem more welcome than kids these days).
Try around Mansfield,and Ollerton , you can always pop along to Whitepost Farm for a day.
At Easter we are off to Wells Next the Sea to Shrublands Cl, and i have a 9 year old and 3 year old( large beaches- narrow gauge railway- perfect).
You could also look around Twycross Zoo area, i am sure there will be loads of CL's, or a bit further would be around Much Wenlock and Telford .. visiting the iron bridge museum is a must.
As a family we have all but given up on CC sites and now rely on CLs onl;y and while the facilities are not the same we have a loo in van , we have shower , a sink, hot water and heating , a football( soft)
Search the CC website for CL's and see what comes up, you can select the facilities you want but we stick to selecting a loo and hook up.
Good luck and don't get too disheartened.
