Scottish Nationalist MPs walked out of the Commons at this week’s Prime Minister’s Questions.

They were protesting against what their Westminster leader, Ian Blackford, described as a “power grab” from the government over Brexit.

The following day, the SNP announced that over 5,000 people had signed up for party membership in the 24 hours since their walkout.

This prompted some eagle-eyed observers to ask: have the SNP now overtaken the Conservatives as the second largest party by membership in the UK?

What do we know about party members?

You might be surprised to learn that political parties are under no obligation to publish figures on how many members they have.

Figures from the House of Commons Library (based on requests to party head offices and press estimates) show that Labour is far and away the largest party – in January 2018, it boasted around half a million members.

But the battle for second place is more hard fought. As of March this year, the Conservatives had 124,000 members, while the SNP had 118,200 in April.

Have the SNP just overtaken the Conservatives?

According to the best available figures, the Tories and SNP were separated by about 6,000 members as of April this year.

Today, Nicola Sturgeon tweeted that in the 48 hours since her party’s Westminster showdown, they’d welcomed an extra 7,526 members to their ranks.

The Conservatives wouldn’t give us any more recent figures than the ones used by the House of Commons Library, but they pointed us to a recent news story that said the party had 124,000 members in March.

So on the balance of the available evidence, we think it’s likely that the SNP have now overtaken the Conservatives to become the second largest party by membership in the UK.

But neither party would confirm to FactCheck their exact number of members as of today, so an element of doubt remains.

But does it really matter?

No doubt the SNP and their supporters will be excited at the thought that they might have overtaken the Conservatives in members.

But it’s not completely clear what this means for their chances of electoral success.

Take Labour and the Conservatives as an example.

Just over 57 per cent of all the people in the UK who are members of a political party are members of Labour. But the party only won 40 per cent of all the votes cast at the 2017 General Election.

Conversely, the Tories do much better than their party membership figures might suggest.

Only 13 per cent of Brits who are members of a political party are signed up to the Conservatives, yet 42 per cent of voters cast their ballots in favour of the Tories in 2017.

And when we broaden the lens to other UK-wide parties, it’s hard to see a clear link between party membership and electoral success.

For example, the Liberal Democrats have about 10 per cent of all party members in the UK, but won just 7 per cent of the national vote – and just 1.8 per cent of the seats in Parliament.

The Greens have 4 per cent of party members, but got just 2 per cent of the national vote – and 0.2 per cent of the seats in Parliament (they’ve only got one MP).

The party membership figures we do have aren’t broken down into England, Scotland, Wales and Northern Ireland, so we can’t do a similar comparison with the SNP (or Plaid Cymru).

It’s also worth bearing in mind that elections to the Scottish Parliament incorporate an element of proportional representation, so the Westminster comparisons don’t translate completely to Holyrood seats.

Nevertheless, while SNP members might be excited to hear that they’ve overtaken the Conservatives, this doesn’t in itself mean the party is destined for a landslide.