This is the structure (courtesy of the FT, hopefully they don't mind with the credit).
The opcos (operating companies, the actual water business) are the three companies inside the bottom right box. They have loads of debt which is secured against all the operating assets (technically against their value rather than the assets themselves as there is a statutory restriction on securing the regulated assets, but it amounts to much the same thing - but some of the details there are in non-public* documents).
The part of the group which is in trouble is higher up in the group structure (the lines denoting ownership by shareholding). Thames Water Limited is the first layer of topco along with the other companies with Kemble in their names.
All the returns earned in the group come from the opcos who run the water business. Everything above them just receives income flows from them in the form of dividends flowing upwards through the structure. As you can see, the two topcos in the lefthand upper dotted box have taken out a load of debt (by selling notes or bonds) - the idea being that they use their dividends to pay the interest on that debt, and take the surplus as profit. But they've stretched themselves too thin and unless they can raise more capital from shareholders, the whole topco edifice is going into administration (which I imagine would take the regulated businesses into a special administration). But, that would also automatically trigger acceleration rights for the lenders to the opcos (acceleration means a right to demand immediate repayment of the principal which has been lent as well as interest). That would put those noteholders in control of realising the value of the opcos. The obvious way to do is to sell to a new topco - either a captive created by the lenders themselves or one created by some other private equity fund. The real problem is that the opcos are the valuable part of the business, and the opco lenders have taken security over them so they have control of a business which fundamentally is still very valuable, it is just its owners who have a problem because they took on too much debt.
Happy to explain more terms but not sure which would be helpful.
*Another thing which should not be permitted with a state regulated natural monopoly even if the privatisation is accepted.