Under EU 261/2004 you are entitled to
A refund of the full price you paid for your ticket within seven days for the part or parts of your journey not made (and for the part or parts already made if the flight is no longer serving any purpose in relation to your original travel plan) and a return flight to the departure airport as soon as possible.
or
Re-routing to your final destination as soon as possible or, if you agree, at a later date. (If the airline flies you to another airport in your destination city then they must pay for the transfer to the airport you were booked for or to another close-by point of your choice)
Now you and BA and easy can argue all day as to what is meant by 'as soon as possible', but I think the option exists. Note that the regulation doesn't say that the reroute must be on the original carrier, neither does it make clear whether the above choice is yours or the airline's (though I understand it's yours).
I would have a look at alternative flights (on any carrier), select the ones that suited me best, and shoot for a reroute. Keep arguing and see where it gets you.
It was a commercial decision taken by grown-up people with expensive suits and £££ signs in their eyes to sell to easyJet. They've made their bed and they can lie in it.