Travel patterns can be affected by a number of reasons. We have enjoyed extremely cheap flights for some time now in particular within Europe so if these prices are affected then naturally it will have some impact although personally, I don't envisage prices would rise by much if they do.
However there is the cost of services and goods, which might rise if it cost us more to trade/ import and naturally it will get passed on to the consumer which in turns means to the guests so might be a bit more expensive for guest. Other factors such as border control, healthcare services are factors that could affect decision to travel as costs add up so for example as an EU member currently I go to France, I’d be entitled to the same healthcare their citizens enjoy including free healthcare whereas that might no longer be the case if we leave the EU.
These are just some of the factors but it's hard to say at the moment as there is still a lot of uncertainty regarding what changes exactly will be made/ the extend of such changes.
I guess time will tell.
Ama