George has answered the other question, so I will give this one a go. You should be fine, provided you both get bills sent to that address; for instance, as long as you both have your bank statements sent to that address then that is proof you live together, even better get a joint account started so they can see you are not just two people sharing the same roof.
If you are apart for any reason, send each other e-mails and keep copies of them. If you get mobile phone statements - some do, you can use these as proof, highlighting each others numbers. Stuff like that goes down well.
May be a daft question, but could you get a stat dec from the ex confirming when you split up and how you haven't been an item since that time. That might help if DIMIA ever question the delay in telling them.
When you do your stat dec, you can explain again why the delay - the family rests etc.
For the next year or so, just relax, enjoy the relationship and DON'T THROW ANYTHING AWAY.
Oh and good luck with Uni.
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