I'm not quite sure what you mean when you say:(posted 9161 days ago)"Is building society allowed to so,"
I think you mean: "Is the building society allowed to repossess if I have paid January's payment after it obtained a repossession order?"
The answer is "yes", although you may be able to stop it by going back to court and saying that you have paid the month's repayment. You'd need to see a solicitor to deal with this.
As it's unlikely that a building society would obtain a repossession order if only January's payment was missing, then making the January payment probably wouldn't make much difference. In that case what really would make a difference is your ability and proposals to pay off any other arrears too.
It's rather hard to answer this one on the information given. I suggest you seek legal advice based on the detail of your case.