Prof Uff adjourned the reconvened inquiry until "overlapping issues" connecting the two tragedies could be resolved.
Mr Finucane was shot and killed by the loyalist paramilitary group the UFF in 1989.
Mr Finucane was shot dead in his north Belfast home by the loyalist UFF in 1989.
The Southall public inquiry under Professor John Uff QC reopened with a minute's silence for the Paddington dead.
The statement does not come as a complete surprise because cracks in the UFF ceasefire have been appearing recently.
The PUP's William Smith blamed the lower Shankill UFF for both attacks, saying that they were intended to sabotage Friday's meeting.
"I welcome the fact that the UFF has re-asserted its commitment to the peace process and the removal of conflict from this society, " he said.
Prof Uff said that he believed he would be able to finish his work before the end of the year without a formal merger of the two investigations.
Mr Hutchinson, whose party has links to the UVF, blamed the UFF for the killing and condemned security forces, who he claimed had left the area open to attack.
David Ervine of the Progressive Unionist Party, which has links with the loyalist paramilitary Ulster Volunteer Force and Red Hand Commando said he did not see the UFF statement as a threat.
The author of the report into the Southall collision published on Thursday, Professor John Uff, said that he believed that there was still "a long way to go" to sort out "inherent problems" in rail privatisation.
Some soldiers did benefit from the Good Friday Agreement early release scheme, but ironically they were the so called "bad apples" who carried out crimes on behalf of either the UVF or the UFF, so therefore came under the aegis of the 1998 Northern Ireland Offences Act.
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