Former Scottish Nationalist MP Michelle Thomson will not face a probe by Westminster's standards watchdog over whether she broke parliamentary rules or brought the House of Commons into disrepute over her property dealings.

A Tory backbencher had lodged two complaints against the party's former business spokeswoman with the parliamentary commissioner for standards Kathryn Hudson.

But after considering whether or not the matter fell within her remit or if there was sufficient evidence to mount a full probe, Ms Hudson has decided not to proceed.

Asked what the reasons were behind her decision, a spokeswoman said: “I can’t comment on the contents of the commissioner’s private correspondence.”

In his letter to Ms Hudson earlier this month, Andrew Bridgen, the MP for North West Leicestershire, said the Thomson case raised “serious questions regarding the professional integrity required from a prominent public servant."

He asked the commissioner to conduct a full investigation into Ms Thomson "and the associated property transactions, that have given cause for concern".

Police Scotland have launched an investigation into alleged irregularities with 13 property deals carried out by a firm in which Ms Thomson was a partner. The deals, which date back to 2010 and 2011, led to her former solicitor Christopher Hales being struck off for professional misconduct.

The Edinburgh West MP has withdrawn from the SNP whip while the policy probe continues; she was the party’s business spokeswoman. The backbencher denies any wrongdoing and has stressed that she will co-operate fully with Police Scotland’s investigation.

Meantime, the Law Society of Scotland, criticised for its handling of the inquiry into Mr Hales, has abruptly axed a debate on the timing of a second independence referendum that it had organised at this week’s SNP conference in Aberdeen because of fears that its impartiality could be called into question.

The body has strongly denied that a pro-independence campaigner on its staff was involved in a year-long delay in issuing a full report to the Crown Office, which then told police to begin an investigation within six days.

The Law Society raised the case twice informally with the Crown Office in December last year and just prior to the General Election in May but did not reveal the names of Mr Hales's clients until after the May poll. It later revealed that it had submitted a report on Mr Hales to the Serious and Organised Crime Agency, now the National Crime Agency, in 2011.

“When will Scotland be ready for #IndyRef2?" was due to take place tomorrow in what was set to be the only debate examining a second poll at the biggest gathering in the SNP's history.

However, a spokeswoman explained: "We were proudly non-partisan during the first referendum. We were concerned about some of the comments made about our fringe event at the SNP conference which made some people call our impartiality into question. That is why we have chosen to cancel this event."

It had been billed that the fringe would "consider the pros and cons of pledging a new poll in the near or the more distant future." SNP leader Nicola Sturgeon has said she believes a second referendum is inevitable but has been reluctant to discuss potential timescales other that predicting Scotland will become independent in her lifetime.

Mr Bridgen was unavailable for comment.