It's very dubious as to whether the UK per se can be said to have "more than two viable parties".
The constituent countries each have a nationalist bloc that will often be successful in local government but not really at the UK level unless whoever is running the UK as a whole is antagonistic to the nationalist position. This results in silliness like Wrexham (which is technically over the border into Wales but nobody there speaks the Welsh language) being required to have Welsh-speaking bureaucrats and signs in Welsh even though the most likely language you'd hear there besides English is... Polish. Why do this? A few million quid on symbolic gestures defuses Welsh nationalism, cheap at twice the price.
But those nationalists won't work together and have almost nothing to say about the UK's larger politics. The closest is probably either the Scottish Nationals objecting to the consequences of Brexit (since Scotland didn't vote for it, and it destroys at least one of the claimed benefits of voting against independence for Scotland in its previous referrendum) or the DUP (a Northern Irish party which opposes Irish independence and is closely affiliated with the Conservative Party) offering a Confidence & Supply deal to keep the Tories in power.
Beyond that, there's the Liberal Democrats, but they aren't very big, and the only time Brits gave enough Lib Dem MPs the nod, they were obliged to throw their lot in with the Tories†, who aren't stupid and used this to ensure most of the blame for the resulting Tory policies landed on Lib Dem MPs who promptly lost in droves. They are nowhere close to being a "viable party" in the sense of able to govern, though they do have majorities in some local governments.
And then what, one Green MP? I mean, she's competent, her policies make sense, all credit to her, but on her own she is not a "viable party" in that sense. Her constituents (Brighton) are going to vote for her because they trend hippier than most of the UK (also gayer, but I don't think the Green Party is especially pro-LGBTQ), because she's good at her job and incumbents are always harder to defeat but that doesn't result in a Green UK government, just one MP.
So no, really there are two viable parties, the Conservative and Unionist Party (Conservatives, "Tories") or the Labour Party. I think they're both a bit screwed because they both subscribe to beliefs about the importance of Work and I believe we're at the end of the era in which the capability of humans to do Work is necessary or perhaps even relevant to prosperity.
† The existence of numerous smaller groups some of which I did not mention means that the Liberal Democrats could not have formed a working coalition with Labour, because that coalition would lack the votes to beat a "No Confidence" motion from Tories and other rival parties, forcing fresh elections. With the Conservatives they had more than enough, so the only alternative to a Tory coalition was fresh elections. In hindsight that would have been the correct choice perhaps, but wisdom at the time was that the one thing voters hated more than the other party was elections, so never force fresh elections unless you're confident you can win them.
The constituent countries each have a nationalist bloc that will often be successful in local government but not really at the UK level unless whoever is running the UK as a whole is antagonistic to the nationalist position. This results in silliness like Wrexham (which is technically over the border into Wales but nobody there speaks the Welsh language) being required to have Welsh-speaking bureaucrats and signs in Welsh even though the most likely language you'd hear there besides English is... Polish. Why do this? A few million quid on symbolic gestures defuses Welsh nationalism, cheap at twice the price.
But those nationalists won't work together and have almost nothing to say about the UK's larger politics. The closest is probably either the Scottish Nationals objecting to the consequences of Brexit (since Scotland didn't vote for it, and it destroys at least one of the claimed benefits of voting against independence for Scotland in its previous referrendum) or the DUP (a Northern Irish party which opposes Irish independence and is closely affiliated with the Conservative Party) offering a Confidence & Supply deal to keep the Tories in power.
Beyond that, there's the Liberal Democrats, but they aren't very big, and the only time Brits gave enough Lib Dem MPs the nod, they were obliged to throw their lot in with the Tories†, who aren't stupid and used this to ensure most of the blame for the resulting Tory policies landed on Lib Dem MPs who promptly lost in droves. They are nowhere close to being a "viable party" in the sense of able to govern, though they do have majorities in some local governments.
And then what, one Green MP? I mean, she's competent, her policies make sense, all credit to her, but on her own she is not a "viable party" in that sense. Her constituents (Brighton) are going to vote for her because they trend hippier than most of the UK (also gayer, but I don't think the Green Party is especially pro-LGBTQ), because she's good at her job and incumbents are always harder to defeat but that doesn't result in a Green UK government, just one MP.
So no, really there are two viable parties, the Conservative and Unionist Party (Conservatives, "Tories") or the Labour Party. I think they're both a bit screwed because they both subscribe to beliefs about the importance of Work and I believe we're at the end of the era in which the capability of humans to do Work is necessary or perhaps even relevant to prosperity.
† The existence of numerous smaller groups some of which I did not mention means that the Liberal Democrats could not have formed a working coalition with Labour, because that coalition would lack the votes to beat a "No Confidence" motion from Tories and other rival parties, forcing fresh elections. With the Conservatives they had more than enough, so the only alternative to a Tory coalition was fresh elections. In hindsight that would have been the correct choice perhaps, but wisdom at the time was that the one thing voters hated more than the other party was elections, so never force fresh elections unless you're confident you can win them.