In general., I'm sure it will not really affect travel to Europe. There may be a visa system coming at some point, like when travelling to the US, but it won't be expensive. Queues will likely be longer, but it's not the end of the world, and getting into Schengen can involve a bit of a queue already. However, should we leave without a deal, then there probably will be short term disruption. I think I read that the channel tunnel has a contingency plan that might involving closing temporarily. I think different airlines have different policies about refunds if flights are disrupted. I suspect that behind the scenes plans are in place to keep things moving, although I guess emergency legislation will be needed. The polls before the referendum were close, and most companies planned for leave to win (eg by hedging against a drop in the pound), and I'm sure the same is happening. The pound is predicted to drop in a no deal, but that's not actually disruptive, it just makes holidays a bit more expensive... even to New Zealand! I'd be amazed if there is a no deal Brexit though.
I've tried to keep that non-political, but I think all Brexit conversations should be banned from here!