Two boys, aged seven and five, whose Filipino mothers claim they were Lord Moynihan's fourth and fifth wives, are laying claim to the title.
Colin Moynihan, 40, the former Conservative sports minister, also has an interest in the outcome of the hearing, because as the half brother of the late lord, he also has a claim. Mr Moynihan wants to stand as an MP again, having lost his Lewisham seat in the 1992 General Election, but cannot offer himself as a candidate for any seat because, if he does become the Fourth Baron Moynihan, he will be elevated to the House of Lords and there would have to be a by-election.
The case had promised an insight into the colourful antics of Anthony Patrick Andrew Cairnes Berkeley Moynihan, Third Baron Moynihan of Leeds, who fled to Manila in 1970 to evade a string of arrest warrants over gambling debts and assorted fraud allegations.
It was known he lived life to the full, building up a pounds 3m fortune from his involvement in the sex industry, and earning himself the nickname of the "Ermine Pimpernel".
But the Queen's Proctor has stepped into the case to challenge the legality of Lord Moynihan's divorce from his fourth wife, Editha, 35, who claims that her signatures on the court papers were forgeries.
This means that the hearing becomes, in effect, a contested divorce case, and Sir Stephen Brown, President of the Family Division, ruled that the Judicial Proceedings Act must apply, and that reporting is strictly limited to names and charges until the judge gives his ruling at the end of the hearing. Lord Meston QC, representing the Queen's Proctor, told the judge the decrees nisi and absolute, granted to Lord Moynihan by Tunbridge Wells County Court in 1990, were void.
It follows that Lord Moynihan's marriage to his fifth wife, former belly- dancer Jinna, was also void because it was bigamous, and their son, Daniel, aged five, is illegitimate and has no claim to the title.
It is also known, however, that DNA tests on Editha's son, Andrew, and samples left by the late lord, show that he could not have been the father.
If both the sons of Lord Moynihan's oriental wives are ruled out, Mr Colin Moynihan will become the Fourth Lord Moynihan of Leeds and will have to set his political sights on a career in the House of Lords.
Lord Moynihan's fortune in the Philippines (he left Britain with virtually nothing) will not be settled at this hearing, but is expected to go to one of the battling wives in Manila.
Details of the High Court battle will have to wait until Sir Stephen Brown gives his judgment at the end of the hearing which is expected to last 10 days.
Although the judge ruled the case came under the Judicial Proceedings Act, the Attorney General's office later agreed that details of the opening could be published. He had told the court how Lord Moynihan fled from Britain facing 57 criminal charges and in March 1970 made an announcement in the Times newspaper that he would never return to the UK.
He said that the first of "a number of remarkable documents" was a marriage certificate in the name of Colin Moynihan, signed in the Philippines, and a woman said to have been the peer's fifth wife, Jinna. Lord Meston said that Lord Moynihan did use the name "Colin" and also had various passports and driving licences in different names.
When the divorce papers were lodged at Tunbridge Wells County Court, the Manila address of Editha, the respondent, was given as Flamingo Health Services, "what is euphemistically called a massage establishment", said Lord Meston.
He asked for his decree absolute to be speeded up so that he could marry Jinna, who was pregnant by him, because he wanted to "make an honest woman of her".
The hearing continues today.