According to the Parliament website the UK Government's majority appears to be -51. Is this correct?

But I thought the Government's majority was one, until Phillip Lee defected, and then 21 were sacked. So I'd expect the majority to be -21.

How should I calculate this?

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    Do you have a reason to doubt this? It is from the parliament website, which is about as official a source as you're likely to get. – CoedRhyfelwr Sep 4 '19 at 13:54
  • I think they've already accounted for the expulsions from the Conservative party that have taken place today and/or yesterday. They have an asterisk under the zero, saying it is a minority government. – Fizz Sep 4 '19 at 13:57
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    Wikipedia's "List of MPs elected in xxxx United Kingdom general election" is typically a good source for this info, as it takes into account the various factors discussed in some of the answers. Here's the current one. – Steve Melnikoff Sep 4 '19 at 15:44
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    This BBC news article explains the breakdown – JCRM Sep 5 '19 at 11:16
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    This question has not aged well... ;-) – Steve Melnikoff Sep 5 '19 at 15:15

There appear to be two key points influencing the difference in your count here:

  1. In a binary choice when 1 voter moves from one side to the other, this shifts the majority by 2. For example if originally 3 vote for A and 2 for B, the majority is 1, when one of the B voters defects it is now 4-1 with a majority of 3.

  2. Sinn Féin MPs do not take their seats for idealogical reasons. This means that 7 MPs are effectively wiped out when calculating notional working majorities, which was the count where the Conservatives had a majority of one.

As noted by CoedRhyfelwr, the list you are using lists the Speaker separately, but doesn't include the 1 other Conservative and 2 Labour Deputy speakers, hence there are only 639 possible voting MPs in play. This assumes no deaths, long term prison sentences, recall petitions or (effective) resignations, which leave a gap until being filled in a by-election.

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    You should also mention that the speaker and deputy speakers do not vote in parliament - that reduces the total by another 4 and makes the numbers add up. – CoedRhyfelwr Sep 4 '19 at 14:09
  • '7 MPs are effectively wiped out when calculating notional working majorities' is that actually done with the official working majority figures? – Pelinore Sep 4 '19 at 14:13
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    @Pelinore There isn't really such a thing as an official working majority figure, beyond any possible result in a potential vote of no confidence. However it is certainly the standard followed by the media. – origimbo Sep 4 '19 at 14:19
  • @origimbo : 'certainly the standard followed by the media' that'll do as a yes for me then :) – Pelinore Sep 4 '19 at 14:24
  • @CoedRhyfelwr Doesn't the speaker vote if there is a tie, and by convention they always vote to maintain the status quo? – Evil Dog Pie Sep 5 '19 at 14:18

Officially, there are 650 seats in parliament. Sinn Féin MPs (of which there are currently seven) refuse to take their seats because they refuse to swear loyalty to the crown. The speaker, and their three deputies do not vote in parliament. This leaves 639 occupied, voting seats, 320 of which are required for a majority. Combined with the fact that the movement of one MP changes your majority by 2, this makes the expulsion of 21 MPs and the movement of one from the Conservatives to the Liberal Democrats reduce the working majority from +1 to -43.

The working majority is, as a concept, the number of MPs required to win a confidence motion, which is why it is useful when working out whether somebody can form a government.

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For starters, maths-wise, if you lose one MP to the opposition your majority goes down by -2.

Now I don't know where exactly the -51 comes from. Politicshome puts it at -43 as of 9 hours ago.

The roll-call of 21 rebel Conservatives from whom the whip has been removed includes [...] Their expulsion leaves Boris Johnson 43 votes short of a majority.

That makes sense since the majority was -1 (319 to 320) right before those expulsions, but after the defection of Phillip Lee to the Lib Dems.

Yesterday, the Parliament website actually listed 320 MPs as Conservatives+DUP (310+10). So subtraction-wise, they did the same math since yesterday, subtracting 21 from the Conservatives, and added them to the independents (which went from 15 to 36).

The "working government majority" is listed as zero on both days on the Parliament's website, even though it was negative. I guess they do this by convention. Also, the Parliament website does not seem to consider the "confidence and supply" agreement as part of the math for the majority. It is listed as zero even for Jul 2, 2018, even though there were 316 Conservatives and 10 DUP back then (together that's more than half the 650 seats). So apparently they only consider a single-party or outright coalition a majority...

On 25 March 2014 (during the Cameron-Clegg coalition) they do list a working majority of 75. Actually the page back then had a more helpful footnote maths-wise:

Government majority calculated as Conservative and Liberal Democrat MPs less all other parties. This calculation excludes the Speaker, Deputy Speakers* (2 Labour, 1 Conservative) and Sinn Fein.

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From MSM they had a majority of 1 before last night & they lost 22 (1 walked across the house & 21 lost the whip) so, 1-44 (each one they lose is another against them so double the losses).

So unless there have been further developments since last night -43 is their current majority.

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