Can I get my deposit back which I paid for on our common law home purchased now that we are separating?
It is not clear from your question whether your (soon-to-be-ex) partner has also supplied a deposit toward the purchase price. In any case, if you are common law partners who purchased a home together, then the laws governing married partners who buy a home together do not apply to you. Once you separate each of you is entitled to take away what you brought into the relationship, and whatever you individually acquired during the course of it. Any item that you purchased or acquired jointly with your partner, is divided.
In other words, the home gets split in the same way as other assets, with the focus being on who contributed what, and who owns what. The value of the home is split in accord with your respective contributions, which in this case means you would get your deposit back.