I think Unity in politics is a false goal. The list of things the parties agree on is huge, but mostly immaterial because it's the things we disagree about that are important and as Parliament is a debating chamber it's no surprise they're talked about far more. Debate may be seem like division, but it's far better than perfect unity - If all our parties agreed on all the issues, it's time to get some new parties. Democracy demands choice.

The incentive to not work with other parties on the things they agree on is a problem I feel comes from using single member consistencies. Working with an MP of another party to achieve something gives them an achievement to list come the next election the candidate for your party won't have, so there's a real conflict of interest from a party perspective in working too closely with a member of another party whose seat is vulnerable (This is more of an issue in US politics but I suspect it exists in the UK too). The way around that is a switch to a multi-member system that would extend that incumbent advantage to all (or at least more) parties, removing the disincentive to cooperate on issues that are agreed upon.