Splintering is death.
The FPTP system guarantees that if two broadly similar parties run candidates in the same seats, they will both be defeated. Effectively the only way that different parties can survive in this ecosystem is to be geographically separated so they don't run against each other. That's a big part of why we see different parties in the other three nations from England, but England is homogenised among two-and-a-half parties.
The last time this was seriously tried was the SDP (due to, inter alia, Europe again). That fizzled out.
There is an argument to be made that UKIP are effectively an external splinter group of the Conservative party. There's a certain amount of traffic between the two, such as disgraced "cash for questions" former MP Neil Hamilton. However UKIP have also picked up some of the even more fringe right people from the EDL and even the NF.
UKIP did a lot better in the European Parliament elections, which are run on the D'Hondt system. (It seems to be part of the unwritten constitution that no two different elected positions in the UK should be run on the same system - we have STV and AMS as well in places!)
The Cameron referendum was supposed to "settle the question" by giving them the referendum which they would lose, quelling rebellion within the Tory party. This backfired badly.
Nonetheless, almost everyone in the party understands: as the united Tory party they are the natural party of governance of England, with the support of the Tory press, regardless of how bad a job they do, provided that Labour can be made out to be a socialist threat. If they split they will be out of power for a generation, until one faction electorally or otherwise obliterates the other. Hence they must hang on like grim death and continue to work with people they have almost total ideological disagreement with and personal hatred for.
(The same also applies to the Labour party, which also has vicious internal divisions over both Europe and Corbynism vs. Blairism, which is why it's not really a functioning opposition at the moment)