Much less regulation back then, very much who do you know approach.
Some might say Thatcher deregulated things a lot. But let's look rationally at this.
A company back then has say £200,000 long-term loans from NatWest and a current account red zone of say £30,000 to cover income variation/struggling debtors/immediate needs/etc. If a new expansion requires more funds than NatWest would want to - or could under NatWest's managers' own limits - extend to them, NatWest might well suggest an approach to a separate (i.e. not part of greater NatWest group) merchant bank.
However if the merchant bank approves the investment to the company there will be a change to the risk scenario facing the company. This new risk scenario is not factored into the original long- and short-term loans given by NatWest to the company prior to the merchant bank's involvement. Accordingly NatWest would like to have additional security for their loans. The company cannot provide any more security than it already has, e.g. deeds of premises, lien on reserve funds, bar on sale of directors' homes, etc.
It is not inconceivable in such circumstances that NatWest may demand an additional guarantee from the merchant bank for the increased risk to their existing loans to the company. After all it is the confidence of the merchant bank in the company that elevated the risk for all banks involved; the prime bank is simply asking the merchant bank to put their signature where their mouth is.
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The Brothers situation the merchant bank and the prime bank are separate commercial concerns. But it's often the case that high street banks have a merchant bank division, e.g. AIIB, IBoI, etc. In this case maybe the elevation of loan risk from prime bank to merchant bank plus the guarantee process is implicit and borrowing companies remain blissfully unaware of it ?