The Exiles were top of their group but the results of their first two matches in Pool Two have been wiped out.
Welsh postponed Saturday's match against Doncaster Knights because they are unable to raise a side.
The Old Deer Park side, who won the competition last season, can appeal against the decision.
A statement from the Rugby Football Union said: "The [British & Irish Cup] Organising Committee's decision was due to the uncertainty of London Welsh's future, its inability to fulfil the next two fixtures and the uncertainty as to whether the club would be able to fulfil its remaining fixtures."
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The judge held that Mr Durkan acted unilaterally and unlawfully in authorising the Belfast Metropolitan Area Plan (BMAP) without securing consent from executive colleagues.
His verdict came in a challenge to the SDLP environment minister's decision.
It was brought by former enterprise minister Arlene Foster of the DUP.
The judge backed claims that because its significance stretched across departmental responsibilities it needed approval from the Stormont cabinet.
A decision on what remedy to grant in the case will be taken at a later date.
BMAP identifies zones for retail, residential and commercial development across the city and outlying areas such as Carrickfergus, Lisburn, Newtownabbey and north Down.
Among the most contentious aspects of the blueprint is a retail zoning which restricts future expansion at the Sprucefield shopping centre to bulky goods only.
That would mean a long-proposed John Lewis store could not be built there.
Mrs Foster, now the first minister, issued proceedings amid claims her colleague in the power-sharing administration breached the ministerial code.
Mr Durkan had said efforts were made to get the issue on the agenda at executive meetings.
During the hearing it was confirmed that the legal action involved a disagreement split down party political lines.
The DUP is opposed to the restrictions adopted by the SDLP minister in BMAP, the judge was told.
Counsel for Mrs Foster repeatedly argued that the planning framework was a cross-cutting, controversial matter which needed the agreement of the whole executive.
He claimed "battle lines were well drawn" in the debate over allowing unrestricted retail development at Sprucefield, with the potential impact on town and city centre shopping.
He alleged the environment minister was only interested in securing approval for his own pre-determined outcome.
The judge was told seven of the other 10 Stormont departments were concerned enough about BMAP to want to take part in a special executive sub-group set up to deal with the issue.
Mr Durkan's barrister contended that attempts were made to coerce him into ignoring his legal duties in dealing with the planning blueprint.
He also claimed the environment minister was put under pressure by DUP ministerial colleagues over a policy which effectively blocked attempts to build a John Lewis store.
However, the judge held that the decision did cut across responsibilities of others in the executive under the terms of the 1998 Northern Ireland Act.
He confirmed: "It was therefore a function of the executive committee to discuss and agree upon it, rather than for the respondent to act unilaterally."
In a statement following the ruling, the Department of Environment said: "DoE planning is carefully considering Mr Justice Treacy's full judgement and the outcome of today's decision."

Colin Hughes was attacked in Old Swan in September 2010 as he went to investigate a noise at the door of his  home.
Two men, aged 18 and 21, from Old Swan and Huyton, were arrested on suspicion of murder on Tuesday.
Detectives have arrested six people as part of the inquiry, but no-one has been charged.
Mr Hughes had been playing cards with his fiancee Paula Greenwood when they heard the glass in the back door smash at about 0045 BST on 21 September.
Ms Greenwood went to call the police while Mr Hughes, a chef at a local pub, went to investigate. She later found him lying face down in the garden.
He was taken to hospital but died soon afterwards. A post-mortem examination found he died from a single stab wound.
London Welsh have been disqualified from the British & Irish Cup after the Championship club went into liquidation on Thursday.
[NEXT_CONCEPT]
Environment Minister Mark H Durkan had no legal power to approve a major new planning blueprint for greater Belfast, a High Court judge has ruled.
[NEXT_CONCEPT]
Two men arrested over the killing of a 42-year-old man in his back garden in Liverpool have been released on bail.