The level of protection depends upon the structure of the underlying fund. Unfortunately the term fund tends to be used to describe a wide variety of collective investments.
Unit trusts, one type fund, provides a high level of protection against the fund managers going out of business as the trusts assets are controlled by a board of trustees, who appoint and remunerate the manager. If the manager goes out of business then the trustees simply appoint new managers.
On the other hand investment trusts are structured like a regular company and offer no trustee protection. You are are shareholder, not a unit holder and it is quite possible for the value of your shareholding to fall to zero.
Vanguard market their funds as UCITS, which unfortunately is another umbrella term used to identify collective investments that are approved for trading with the EU, that have a variety of underlying structures. However, as I understand it, the UCITS regulations require a structure similar to that of unit trusts.
"A requirement on Member States to ensure that assets held in custody by a depositary or its delegate are protected in the event of the depositary or its delegate becoming insolvent" https://www.fca.org.uk/firms/authorised-recognised-funds/ucits-v-new-requirements