The proposal was supported by Liberal Democrat peer Lord Shipley, crossbencher Lord Best and the opposition.
Crossbencher Baroness Mar said micro-chipping dogs at birth would prevent the "iniquitous practice" of puppy farming.
Crossbencher Lord Digby Jones, a former trade minister under Gordon Brown, agreed with Lord Hoyle.
Lord Henley agreed with crossbencher Lord Forsyth of Drumlean that most of the participants were "part-time protesters".
Her amendment was supported by several peers including Labour's Baroness Wilkins and crossbencher Lord Low of Dalston.
First to give a speech was crossbencher Lord Bichard, who focused on standards of behaviour within local councils.
There's also a short debate on ethical and sustainable fashion led by the crossbencher, Baroness Young of Hornsey.
But crossbencher Baroness Deech questioned whether ministers were aware of the number of unreported incidents that took place.
Crossbencher Lord Owen said Lord Marks had "succinctly explained what this bill needs".
The bill will be piloted through by the Crossbencher, Lord Stevenson of Coddenham.
He was backed by two human rights lawyers: crossbencher Lord Pannick and Labour peer Baroness Kennedy of The Shaws.
Diplomat and crossbencher Lord Hannay of Chiswick called the government's plan to repatriate powers from Brussels "a futile displacement activity".
Labour's Baroness Gould of Potternewton focused on HIV-Aids diagnosis, before crossbencher Baroness Masham of Ilton highlighted "hard-to-reach" sufferers of tuberculosis.
Her calls were back by another crossbencher, Lord Imbert, who suggested mandatory sobriety tests for those convicted of alcohol-related offences.
Crossbencher Baroness Finlay of Llandaff argued that the bill placed too little emphasis on treating those with rare or complex conditions.
Peers also passed crossbencher Baroness Grey Thompson's regret motion on access to legal aid for disabled people by 163 votes to 148.
The exchange followed a question from crossbencher Baroness Cox on protecting the human rights of ethnic Burmese people, on 13 October 2011.
Crossbencher Lord Stern of Brentford and Conservative Lord Bates both argued that there was scope to spend even more on development aid.
Baroness Butler-Sloss, another crossbencher, suggested the government should ask the Law Commission to examine ways of modernising the way legislation is presented.
Crossbencher Lord Dear, who led Lords moves in 2008 to veto 42-day pre-charge detention, said the current DPP's views should have "considerable weight".
Crossbencher Baroness Manningham-Buller said allegations that expenses had been abused had "eroded trust, not only in the House of Commons, but also here".
Another crossbencher, Lord Walton of Detchant, asked what action the government was taking to improve patient access to new treatments for multiple sclerosis (MS).
Crossbencher Lord Adebowale said young adults were "significantly over-represented" in the prison population, with "very high" reoffending rates following often short periods in custody.
Former judge and crossbencher Baroness Butler-Sloss agreed, claiming that, unless the cross-party amendment was accepted, a "large number of victims" would "fall through the net".
His wife, Baroness Hogg, sits as a crossbencher in the Lords having been made a life peer by former Tory Prime Minister Sir John Major.
Crossbencher and former hospital consultant Lord Patel said the new body must be seen as an independent "big hitter" rather than being an "obscure" sub-committee.
Crossbencher Lord Harries of Pentregarth then asked the government what means it has to hold Interpol to account, especially where United Kingdom citizens are involved.
Crossbencher Lord Northbourne introduced an amendment to the bill outlining parents' responsibility to promote their children's "personal, social and emotional development" before they reach primary-school age.
The government accepted amendments put forward by crossbencher Lord Pannick that would give security officers at the Supreme Court the same powers as those at other courts.
Crossbencher Lord Burns, who headed the committee of inquiry into hunting, told peers that he didn't want to express a view on whether foxhunting should be banned.
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