Capital Gains Tax (CGT) is a tax on the increase in value of something during the period you have owned it. CGT may be due when you sell, give away, transfer or otherwise dispose of something. There may be CGT payable on a transfer of property between you and your partner or on a sale of the property.
In general, there is no CGT when you dispose of your only or main home (or your share in it). So, transferring or selling your share of the home to your partner at the time you split up is likely to be free of CGT. But the situation is more complex if you move out and make the transfer or sale later on. There may also be CGT to pay in some particular circumstances, such as if you ran a business from home. See Managing money – tax.
In some situations, you may also need to consider inheritance tax (a tax on the value of things you give away). See Managing money – tax.
This is a complex area and you should speak to a solicitor and/or a tax adviser to see whether you will need to pay any tax so that you can take this into account when discussing a financial settlement - see Useful links.