The recent crisis at BA has brought into focus what might happen should something like this occur post Brexit.

At the moment consumers have a certain amount of protection under both Regulation 261/2004 and the Package Travel Regulations, both of which came out of Brussels and have been adopted by all EU member states
If we take the BA crisis, the general rule of thumb would be:
Regulation 261/2001 makes the airline pay for:
If the flight is delayed longer than 3 hours due to ‘exceptional reasons’ the airline has to provide refreshments and some compensation (depending on the length of flight (in kilometres).

If the airline cancels the flight they have to offer a choice of either a refund of the ticket or an alternative flight.

The regulations will not cover you if you choose to travel from a different departure point or to a different destination than your original booking, you can’t claim compensation for any expenses incurred for travel between these or any other consequential expenses, e.g. car hire, parking costs, etc.

Package Holiday Regulations (PTR) apply if you have booked more than two elements of a holiday with the same provider, (for example flight and car hire or flight and accommodation), as this then classifies the holiday as a ’package’ and the provider a ‘tour operator’ who is then responsible for:
Providing alternative arrangements or refunding your money
Providing bed and breakfast accommodation if your return journey is delayed due to force majeure

However, many people book their flights and accommodation separately and so they fall outside the protection of PTR. The advice to these customers generally, is “contact your travel insurer”.

But there are some elements of this situation that are not covered by standard travel insurance policies, for example:
Whilst the airline might refund the flight costs, other costs such as accommodation might not be covered if you cancel the trip because the airline has cancelled your flight.
Assistance with the additional costs of accommodation and food should you be stranded in resort because of a situation like this
A contribution towards additional costs of car parking/dog kennelling etc. should travellers be delayed on their return journey.

However, post Brexit this could all change as both Regulation 261/2004 and the PTR are both EU directives, and might become redundant once we formally leave the EU. If this were the case then one might envisage consumers needing greater cover under their travel insurance.
In order to meet this demand for more cover, insurers would have to amend their policy wordings, and this could lead to an increase in premiums.
Consumers traditionally buy their travel insurance based on price rather than looking at the cover they actually need.
A post Brexit world sans EU travel directives might just change this buying habit.