Anniebach
Nominations are predominantly put forward by the Political Parties themselves for their own MP's. The seat left on the Justice Committee was a ' Labour Party' seat.
Nomination requirements
To be valid, nominations must:
Contain a signed statement made by the candidate declaring their willingness to stand
Be accompanied by the signatures of 15 MPs elected to the Commons ' AS MEMBERS OF THE SAME POLITICL PARTY 'as the candidate (or 10 per cent of the MPs elected to the House of that party, whichever is the lower). More than 15 signatures can be collected but only the first 15 valid signatures are printed.
Nominations may be accompanied by the signatures of up to five MPs elected to the House as members of any party other than to which the chair is allocated or of no party. Similarly, only five such signatures are printed.
Candidates must declare 'ANY RELATIVE INTERSTS' with their nomination.
As for your link Rigby 46 that was not a vote of confidence in Keith Vaz! It was more to do with parliamentary precedence. A vote was allowed to basically vote 'No Confidence' in the nomination of Vaz to the Justice Committee. It went in Keith Vaz favour not because they though he was a good nomination but if this became a precedent then every time somebody took umbrage with a nomination they could be given a vote of 'No Confidence' willy nilly and it could easily become a political tool to use against the opposition party.
So it was the decision of the Labour Party to allow his nomination .
Perhaps this explains it better.
www.bbc.co.uk/news/uk-politics-parliaments-37859080
extract
"The normal deal is that the political parties in the Commons choose the MPs who are nominated to their party quota on select committees, by their own internal process, and the other parties automatically approve their choice.
The argument is that if the parties start tinkering with each other's nominations, that way, madness lies. So no fan clubs were involved in the making of this particular appointment,".
Covers both points, the nomination system and why the Tory vote was not a vote of confidence in Vaz but all about parliamentary precedence.