If you were not married or in a civil partnership, then if there is a change in the income of either you or your former partner, you would not be legally entitled to make claims for maintenance against each other. However, you may be able to increase (or reduce) any maintenance payable for the benefit of any children either through the Child Support Agency or through the court (see If you have children).
If you were married or in a civil partnership, and you are experiencing difficulties managing on the amount of income you have, or if the income of the person who pays maintenance has increased significantly, then it may be possible to have the maintenance paid to you and/or the children increased. In the same way, if you pay maintenance to your former spouse or civil partner and your income position worsens, you can ask for the level of the payments to be reduced. If you cannot reach an agreement directly, then an application to the court to increase or reduce the payments will need to be made. You should speak to a solicitor to see what your options are.
If the capital position of the former spouse or civil partner who is paying maintenance improves so that there is enough cash to do so, it may be possible for maintenance to be "capitalised". This means that the person who receives maintenance would get a lump sum to provide them with an income instead of ongoing maintenance payments.