Thank you for your response and attachment that is most helpful.
In response to your enquiry whilst there is nothing stopping your wife actually making an Application to Join you here in the UK as your Spouse, all the requirements must be fulfilled including that you fulfill the financial requirements as her Sponsor.
Crucially, there are a set of questions on the VISA Application process that could cause a problem, also if the UK VISA authorities find out that your wife made a fraudulent application to Ireland this could jeopardise her UK VISA Application.
In short nothing stopping your Wife from making the Application but "honesty is the best policy" because if the authorities find out that your wife has lied or misled them on her UK Visa Application, your wife could be banned from making any future application for many years.
Unless, I can help you further , Please will you provide a 5* Star Rating for which I will be most grateful.
If you do need more information, please request a Telephone call as this is a complex area of Law.