Updated June 7, 19:45 BST: On Tuesday night, 444 MPs voted in favour of the third reading of the Investigatory Powers Bill. The SNP, Liberal Democrats, and the Green Party opposed the proposed law representing just 69 votes. The bill will now proceed to the House of Lords.

Original story (evening, June 6)

The UK government's bid to massively ramp up surveillance of Brits' Internet activity has been supported "in principle" by the Labour party after it claimed that "significant demands" were met by home secretary Theresa May.

Labour's shadow home office minister Keir Starmer told MPs during day one of the report stage of the draft Investigatory Powers Bill that his party had undergone a "constructive engagement" with the Conservative government, which led to a number of changes within the proposed legislation.

"The government has moved in response to those demands significantly... and I’m not doing this as a list of victories, or scalps, or concessions, or u-turns," Starmer, who is the UK's former director of public prosecutions, told the House of Commons on Monday evening during a lengthy, ongoing debate.

"Actually they were significant, we made those demands, we stuck by them, and in fairness the government has responded on them in the right spirit in relation to the ones we know about."

He had earlier told MPs: "Safety and security and human rights are not mutually exclusive, they are not either/ors, and we can have both. And that is why Labour has supported the principle of this new bill, but it's also why we have focused intensely on the necessity for the powers in the bill and the safeguards."

Starmer reiterated what was first revealed publicly by Theresa May in November last year—Britain's spooks have, for years, been using section 94 of the 1984 Telecommunications Act to intercept bulk communications data of people in the UK:

The bulk powers are available and being exercised at the moment under the existing arrangements, by and large—there are some exceptions—therefore what this bill does is put them onto a statutory footing with proper safeguards.

Starmer added that Labour was seeking to "tighten up" human rights references in the draft law, but also pointed out that, post Edward Snowden, "it is important that the powers being exercised are avowed, it’s important they are placed on the statute."

Letters between home office minister John Hayes and Starmer had helped secure an agreement to review wide-ranging bulk powers proposed within the IPB, the Labour MP said.

Hayes went on to tell MPs that "it is important this review is conducted during the period this bill is being considered." It means a report from the UK's terror watchdog David Anderson QC is expected to be published within the next three months—ahead of the bill's passage through the committee stage in the House of Lords.

The Scottish National Party's home affairs spokesperson Joanna Cherry told MPs that she was happy to see that an independent study of bulk powers would be carried out, but added that the remit of the review was yet to be confirmed.

She told MPs:

The government will have to go an awful lot further before the Scottish National Party can contemplate giving this bill our support. It’s a good idea to consolidate the powers and have a modern and comprehensive law. But we remain concerned about the legality of some of the powers that are still on the face of this bill and the fact that they very significantly exceed what was on or what is authorised in other Western democracies, for example, the retention of Internet Connection Records.

Cherry said that the SNP refused to support the bill because so many of the party's proposed amendments had been opposed or ignored by the government. She added that MPs had not been given enough time to scrutinise the planned spying law.

"We're not going to get a chance to vote on more than half of these amendments," she said, and claimed only eight or nine amendments would be voted on, given the time restraints. "It’s not the way to legislate," Cherry said.

In the past hour MPs have been voting on proposed amendments to the Investigatory Powers Bill.

At time of publication, the following had been rejected:

Clause 1: gives IP commissioner power to notify an individual of an interception warrant of the existence of the warrant after it has fallen. (64 ayes; 278 noes: a majority of 214.) Amendment 465: to establish an Investigatory Powers commission. (64 ayes; 281 noes: a majority of 217.) Amendment 482: protect whistle-blowers and those making unsolicited disclosures from criminal prosecutions. (67 ayes; 281 noes: a majority of 214.)

Hayes went on to lobby the house to support the government's proposed amendments to the bill.

Shadow home secretary Andy Burnham then took to the dispatch box to confirm that Labour will support the government's amendment to the judicial review test. He told MPs: "We believe this does indeed amount to a real double lock and I have to say this is a real victory for this side of the house."

Labour, it's worth remembering, has long supported ramping up online spying in the UK.

IPB amendment votes ended close to midnight on Monday. There was little opposition to the draft law, after Labour abstained from voting during the report stage of the bill.

Two other amendments were rejected:

Amendment 267: seeks to narrow the scope of “thematic” warrants by defining a premises or subject matter for the warrant. (67 ayes; 271 noes: a majority of 204.) Amendment 312: requires “reasonable suspicion of serious crime” before a warrant for interception is approved. (66 ayes; 272 noes: a majority of 206.)

At the end of the debate, Hayes heaped praise on Labour for supporting the thrust of the bill.

And Labour was in celebratory mood with Burnham claiming that "major concessions" had been secured by his party, including what he described as "a historic commitment that trade union activities cannot be considered sufficient reason for investigatory powers to be used." He added that a privacy clause had been "placed at the heart of the bill."

MPs will return to debate the Investigatory Powers Bill on Tuesday, after which time it will wing its way to the House of Lords.