THanks BHDBOY for saving me having to spell it all out. ^

As someone whose work brings him in contact with the immigration systems of both Ireland and the UK, I can tell you that there is sporadic immigration checking at the border and at train stations both north and south of the border.

To the OP, a refusal by the UK Border Agency does not bode well for arrival in Ireland. As mentioned above, due to the common travel area, there is a great deal of shared information between both jurisdictions. That said, it does not preclude entry. You'd need to have all your ducks in a row and a pretty convincing story, with sufficient backup available. Applying for an Irish visa, might be indicated - why not contact your nearest Irish embassy?