We live in the East Midlands so thought it would be nice to check out the Norfolk coast (I love beaches!). Never been before and stupidly didn't check prices or availability. We wanted to go for a week in June but having checked the area around Wells next the Sea, which looks walkable to the nature reserve, all self catering and caravans are booked. Only accommodation left is camping pitches or very expensive b and b. I had this dream of just walking to the beach with baby and dog in tow, then lazy pub lunches, exploring a naice village etc...
I feel like such an amateur. DH and I have never actually been on holiday 
Is there anywhere in Norfolk we can do this type of holiday on a budget in June 2017?
If not please suggest somewhere else not too far away that we could?
Thanks!