Hi Neil,
Thanks for taking the time to check out our plugins 🙂
So it sounds like both Event Tickets and Event Tickets Plus may be of interest as a way of letting your customers making bookings (for free or by paying).
Events created with The Events Calendar – as with WordPress posts generally – are “oEmbeddable” and so can indeed be embedded into other websites, even if they are not powered by WordPress, however the ticket form itself is not directly oEmbeddable. That said, we pride ourselves on producing code that can easily be extended, so if you were willing to invest in a modest amount of custom development work I’m sure you could use our existing plugins as a solid foundation on which to build a working solution.
I hope that helps, but do let me know if you have other questions.