If you were not married or in a civil partnership, then a new relationship will not impact on your financial rights or obligations towards your former partner.
The position is different if you were married or in a civil partnership. If you receive maintenance for yourself and you then live with another person, then your former spouse or civil partner could ask you (or the court if you refuse) to reduce (or terminate) the level of the maintenance being paid, usually on the basis that there is someone else who is contributing to your household expenses. Living with someone else does not automatically bring maintenance to an end, and you should speak to a solicitor (see Useful links) before making an application to the court. If you re-marry, any maintenance you receive from your former spouse or civil partner will automatically end.
If you plan to live with your new partner you should consider entering into a formal agreement with them about what would happen if the relationship ends, for example in relation to finances and any children you may have. If you get engaged or plan to marry or form a civil partnership then you should consider entering into a pre-marital or pre-civil partnership agreement so that you can agree what happens in relation to finances and any children you may have in the unfortunate event that the relationship ends.
When you form a new relationship you should consider making a new Will so that you can be sure that your estate will pass as you wish in the event of your death and that suitable provision is made for your new partner if appropriate as well as any children.