We've just got back from a fab week in Clacton, whole family with 12yo, 6yo and 8 week old! We got lucky, the weather was fabulous, so Martello Beach was nice for a day and we walked from their to the pier for fish and chips. We did an evening on the pier rides (bands for the rides were cheaper on Friday pm) and went to the Martello Children's Zoo (a petting zoo in the old observation tower about 15 min walk with LO and buggy from the pier). We were staying in Jaywick so went crabbing there a couple of times. All you need is a net bag (like the ones washing tabs go in) filled with leftover meat (we used sausages!) attached to a long bit of string and a bucket. We caught 20+ crabs each time and everyone loved it! (We did let them go after we caught them! We also went into Colchester (about 20 mins drive) and visited the castle and the Zoo. Both were excellent but zoo is quite expensive. Hope that helps and have a great holiday!
You can get the foot ferry from near the park to Brightlingsea where there is a nice beach and paddling pool at the end of the beach huts, there is also a play park, open air swimming pool and a few cafes. The ferry jetty is also good for crabbing. Walton on the Naze is a good day out. Have fun.