The case's importance derives partly from its historical context, with the South Sea Bubble. Lord King LC, who decided the case, replaced the former Lord Chancellor, Thomas Parker, 1st Earl of Macclesfield who was tried and found guilty of accepting bribes in 1725. The remedy of granting a constructive trust over property, and the strict approach that all possibility of a conflict of interest was to be avoided, derived from the general outrage at the time.
A child had inherited the lease on Romford Market near London. Mr Sandford was entrusted to look after this property until the child matured. But before then, the lease expired. The landlord had told Mr Sandford that he did not want the child to have the renewed lease. There was clear evidence of the refusal to renew for the benefit of the infant. Yet the landlord was happy (apparently) to give Mr Sandford the opportunity of the lease instead. Mr Sandford took it. When the child (now Mr Keech) grew up, he sued Mr Sandford for the profit that he had been making by getting the market's lease.
A person being possessed of a lease of … a market, devised his estate to trustee in trust for the infant; before the expiration of the term the trustee applied to the lessor for a renewal for the benefit of the infant, which he refused, … there was clear proof of the refusal to renew for the benefit of the infant, on which the trustee sets a lease made to himself.
I must consider this as a trust for the infant, for I very well see, if a trustee, on the refusal to renew, might have a lease to himself, few trust-estates would be renewed to the cestui que use; though I do not say there is a fraud in this case, yet [the trustee] should rather have let it run out, than to have had the lease to himself. This may seem hard, that the trustee is the only person of all mankind who might not have the lease: but it is very proper that rule should be strictly pursued, and not in the least relaxed; for it is very obvious what would be the consequence of letting trustees have the lease, on refusal to renew to cestui que use. So decreed, that the lease should be assigned to the infant, and that the trustee should be indemnified from any covenants comprised in the lease, and an account of the profits made since the renewal.
Mr Sandford was meant to be trusted, but he put himself in a position of conflict of interest. Lord King LC was worried that trustees might exploit opportunities to use trust property for themselves instead of looking after it. Business speculators using trusts had just recently caused a stock market crash. Strict duties for trustees made their way into company law and were applied to directors and chief executive officers.
The influence of Keech has reached beyond the duties of trustees, into the fiduciary duties of company directors. The approach being taken in England (c.f. the position in Delaware corporate law) is that any possibility of a conflict of interest means a breach of trust.
Bray v Ford  AC 44 at 51-52, per Lord Herschell, the no possibility of conflict rule is “based upon the consideration that, human nature being what it is, there is danger of the person holding a fiduciary position being swayed by interest rather than duty….”