Your ownership and title would not be affected, although there would likely be a short delay before you could realise its value, while a liquidator was appointed.
A liquidator could not claim title to your bullion. That’s because you are the legal owner of all gold, silver, platinum and palladium that you buy through BullionVault. BullionVault is acting as a custodian, which is a status that's very different from your bank, and immeasurably safer for you.
With a bank account, you transfer ownership of your money to the bank when you make a deposit. Your money then appears on the bank's balance sheet, and you become its creditor. The bank would become insolvent (and fail) if there were insufficient assets to meet the liabilities owed to all its creditors, and that tends to happen to banks periodically because their business is to lend your money for profit, not simply keep it in a vault.
You have not made a deposit of gold to BullionVault. You are not BullionVault's creditor and do not appear on its balance sheet. Technically your gold, silver, platinum and palladium is the subject of a bailment - a legal status through which physical property remains yours while it is in the care of another. A liquidator cannot consider it an asset of the company, so would have no claim over it and must return it to you in full.
BullionVault's finances are very strong. Very few companies maintain debt free cash and bullion reserves - available at short notice - sufficient to cover the gross costs of running their operation for five years without any revenue. The standard equivalent requirement for the banking industry is 3 months.