Okay, I think that I have found the answer to my own question.
TLDR: Parliament technically has the power to summon / fine / imprison anyone, but the applicability of these laws is in doubt as some have not been exercised for 100’s of years. It is unclear that any fines or imprisonment would actually have been brought against the man.
It turns out that The House of Commons and The House of Lords technically have the power to summon, imprison, and fine anyone. (See point 252 on page 62 here)
An older BBC article goes over these alleged powers in greater detail. The last time that an non member was summoned was in 1957:
”The editor of the Sunday Express, John Junor, was brought by the Serjeant at Arms to the bar and admonished by the Speaker for publishing an article that cast doubt on the integrity of MPs over their constituency petrol allowances.”
However, the powers of fining and imprisonment have not been exercised for 100’s of years and their legitimacy today is debatable. Specifically, the European Convention of Human Rights would seem to undermine such arbitrary powers of imprisonment.
The article alleges that the last recorded cases of fines or imprisonment are as follows:
”There is a former cell in the lower floors of the clock tower. But in practice it is only the police within the parliamentary estate who have the right to arrest anyone. The last time a non-MP was imprisoned was in 1880 when a man called Charles Grissell was detained.”
”The last time MPs fined someone was in 6 February 1666 when a man called Thomas White was forced to pay the House £1,000 for preventing an MP attending parliament.”
So I’m summary, it is murky territory and highly unlikely that the business man in question would have faced serious fines or imprisonment for failing to comply. This parliamentary article nicely summarises how farcical the whole affair could have become:
”In modern circumstances, as a televised proceeding, it would risk being a pantomime. Consider: the miscreant is brought to the Bar, accompanied by the Serjeant with the Mace, and is admonished by the Speaker in front of the House. Even assuming that the miscreant is prepared to come (and a refusal would be a further embarrassment) the proceedings are not controllable, and the House would risk looking like a lynch mob. The Speaker stands and delivers a rebuke, at a range of some thirty yards. Then what? The individual at the Bar, in prime TV time, may decide to have a go at the House and the treatment he or she has received. If the individual really does have a case, or perhaps produces some surprise piece of evidence which makes it clear that the House has got it wrong, the result could be a reputational disaster.”