They will get moved on within about 4 weeks if you and your neighbours pester the council every day. This looks like council land which should make it relatively straight forward. If a local team rents the pitch let them know because it looks like a local asset has been removed and will unquestionably be ruined.
Your council will have a traveller liaison officer who you should contact. The more pressure you put them under the better.
Lay it on thick that they are littering, loud, exposing themselves to children when they go to the toilet, their generators are keeping you awake, you’ve seen rats, you’ve been verbally abused, you have seen a traveller in your back garden looking through your window, kids have been throwing stones etc..
Sadly most of this will be true anyway
Brace yourself. It’s going to be a shit few weeks and your nice field will be destroyed.
Long term the most important thing will be to work our how they got there and to make sure they never get the chance to return.
After they are removed they will get a fixed time period when they aren’t allowed to return and it will be crucial to put unmovable barriers in the way to prevent their return. Remember they will have heavy equipment so the council need concrete boulders or something similar.
If you don’t do the above they will be a regular feature I’m afraid.