Firstly - Congratulations!
I just had a search and can't find any elopement packages in Esex - why don't you try contacted some licensed venues and discuss your plans with them? If you are happy to go for a midweek wedding, it would be cheaper, and they would probably be able to accommodate you, as they will be busy with big weddings on the weekends, and probably won't want to give up the chance of making a ton of money.
Also, I found this photographer who is based in Essex and specialises in elopement wedding photography - why not contact her and see if she can help you?
Good luck! X