My ex-partner and I bought a house together. After our separation, we put it on the market, but unfortunately, we didn't receive any reasonable offers. Following the separation, I bought another house. Now, I'm starting to feel stuck because I have two mortgages to pay off. So, what would the consequences be if I were to "hand in" the keys to my first house on my credit report? And how long would these consequences remain on my credit report?

Your credit score will be significantly affected by the payment default on your first home, and this information should remain on your credit report for seven years.

However, this does not give the mortgage lender on your second home the right to repossess it if you are not in default on that mortgage. But it could negatively impact you when it comes time to renew that mortgage.
It remains to be seen whether the mortgage lender on your first home will limit themselves to a mortgage lien or pursue a personal lawsuit against you. That is their choice. If they pursue a personal lawsuit, you may have to consider bankruptcy or a proposal.