If your wife would retain the capital in the property then I would be surprised if HMRC would accept that you could effect a transfer of the right to the income to you as you propose (if necessary, HMRC might be able to rely on the settlements legislation).
From the mortgage company's perspective I'm not sure how they would determine (or be interested in) who is declaring the income?
I'm speculating but I suppose examples might be:
Being interested whether another person has any beneficial interest in the property that could affect their security (overreaching).
Being interested in whether there is any tax evasion given that they might be in receipt of any dirty money being used to repay the loan.
General breach of lending terms and conditions (particularly if deliberate).