Ha! Rebook an EZY flight? Watch the fees pile up on that one, and it doesn't really make much sense, as EZY doesn't serve LHR. An LHR-LGW transfer from a legacy carrier to a LCC is not advisable. Honestly, it's not advisable to do it strictly within LGW if you haven't left a large amount of time to allow for delays of the inbound aircraft.

I think the OP's best option is to get a refund, with which DL should be immediately forthcoming. The only SkyTeam carriers serving LGW now are VN and KE (not at all helpful in this case), UX (going to MAD and then up to LGW is not likely going to work out timewise), and AZ on AP codeshares (again, timing won't be good). The OP will be better off rebooking on US (or BA or VS if coming from one of the few cities they serve in the US via LGW).