You do need a licence for crays, you get one from the Environment Agency. Depends on the area of the country and what problems are happening in that area with American crayfish and number of natives. If you have a decent population of native, you are unlikely to get a licence.
As for eels, unless you have been licensed since 2008, you will not get a permit.
I have made bottle traps for shrimp in the past to catch them in the estuary to use them as bait for Flounders but not to eat.
If you want net, use these chaps:
http://www.advancednetting.co.uk/shop/catalog/
If you can describe to them what you want it for, they will recommend the best for you. Works out much cheaper if you were after a long net to buy sheet netting and braid from them rather than spending £100+ on one 50 yard net.