Well, I can understand that they would not automatically transfer the booking over to Easyjet if there is a connection, as Easyjet is strictly point-to-point. Still, very poor form of them to contact you that late and without offering a solution. According to Reg 261/2004, however, they have to offer re-routing under comparable transport conditions to your final destination at the earliest opportunity (or reimbursement, or rerouting at later date, but then subject to availability). The choice between those three options is yours, not theirs. So if you want re-routing, you should be able to insist on it.
If I were in your shoes and there was no alternative tickets that can be purchased at a reasonable price, I would press the issue on the duty to offer re-routing under Art 5(1)(a) and Art 8(1)(b) of Reg 261/2004.