In the UK, they have a system, whereby people who do not have a big income can purchase a portion of the house (normally 50%). The other portion of the house is then rented to the buyer at a discounted market rate. The Government subsidies the rent. The other portion of the house will still belong to the owner of the building. (This system is called SHARED OWNERSHIP, i.e., tenant owns 50%, and owner owns the other 50%). I bought 50% of the house using a Bank loan, so there are 2 payments, one to pay the 50% of the house to a Bank, and the other is to pay the discounted rent to the owner of the building.
After finding out that it is Haraam to take out a loan from the bank and pay interest on it, I decided to sell my portion.
In doing so, there was some increase of the value of the house. This increase is then split 50% between me and the owner of the building.
What should I do with this money? Is it Halaal to use it? Or just give it away to good causes?
An example is below:
Cost of house is 10,000
I bought 50% (5000)
I pay bank loan payment on the 5000, and rent on the other 5000. When I want to sell, the house value is now 12,000. So the owner takes 6000 and I take 6000. After I re-pay the bank the loan, I am left with 1000.
What should I do with that money (1000)?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

Whoever buys a house or a portion of the house with an interest loan, has indeed committed a great sin that requires one to repent to Allaah. However, it is not one of the conditions of repentance to sell the house that one bought with an interest loan; it is enough for the debtor to sincerely repent and regret what he had done. It is confirmed that the Prophet said: "Whoever repents from sin, is like the one who has not committed any sin." [Ibn Maajah]

So you correctly owned the house and you can keep it or sell it, and it is lawful for you to sell it at the same price than you bought it, or at a greater or lesser price. We have already mentioned that a debtor with an interest loan is not obliged to sell what he has bought with that loan, because when one gets the loan, it becomes his property and it is a debt on him, whether it is an interest-based loan or otherwise; however, one is sinful for getting an interest-based loan.    

Allaah knows best.