I've tried bringing my flight forward in Dublin before, both at the check-in desk and the gate, and it didn't work. Doesn't mean you shouldn't try but just thought you'd want the datapoint.
Also I should point out that your choice of turn-around is much more risky because if your outbound flight is cancelled, which can happen with morning Domestic/Irish flights, then you're completely stuck. Whereas if you were doing a back-to-back then your DUB-LHR would be cancelled in this situation too. Not criticising, just wanted to point out why people do this. And also DUB really is very easy for B2B, particularly during the day when you can use flight connections.