Companies House have no power to remove a Director
Companies House are in practice exempt from the Government rules that Banks and others have to follow for KYC (Know Your Customer) and AML (Anti Money Laundering)
Companies House do not check if a Director is disqualified by bankruptcy and if notified they still cannot remove the person from the Register nor inform the Insolvency Service. Following is the Boilerplate sent by Companies House if violations are reported :-
"Companies House (CH) have limited powers and our main role under current parliamentary legislation only allows us to register and display information to the public. We do not have any powers of investigation beyond requesting that a director who is disqualified or is an undischarged bankrupt, terminates their appointments to active companies."
This failure is the partial reason fro many frauds and happened due to business lobbyists who would prefer companies house to be toothless and underfunded.
From my limited Knowledge I think the Insolvency service is more competent