They can still get access to LHR, the only difference is that they will be code sharing on BA's flights rather than running the flight themselves, which would be more profitable due to less competition...
BA have being code sharing with EI for years and still are BTW so why would EI code share with them when BA would be unable to provide 12 or 13 daily flights depending on season that EI can. BA are only on DUB route because they took over from BMI and currently have nothing productive to do with the slots or aircraft which is why they are operating the route. BA can't be bothered even offering there own flights for passengers who are connecting from DUB at LHR only the EI ones are offered. It says a lot don't you think...