Brits make 50 million visits to Europe every year1. 1.4 million Brits work, study or have retired abroad in the EU2,3. That's 12 times as many as go to anywhere in North America, and 5 times as many as go anywhere in the world. When abroad, Brits get free emergency healthcare via the European Health Insurance Card4,5: a scheme we use more than most as a result of our high rate of excursions, saving holidaymakers a lot of paperwork and expense compared to the costs of organize it country-by-country. As a result of the EU's bargaining power with providers, ordinary class plane flights are 40% cheaper5 in the EU and EU-wide travel assistance and compensation schemes help many2,6.
After living abroad for 5 years, Brits get free health care anywhere in the EU6. Our driving licenses are valid throughout the EU2,7, we can go work (and retire) anywhere in the EU6 (does anyone remember how awkward (and often impossible) it was to organize work Visas?), and, anywhere in the world we can use the embassies of EU states in the absence of a UK embassy6. Membership of the EU facilitates harmonised motor insurance, vehicle registrations, number plates and other aspects of travel, and in each case, this saves individual time and expense7,8. Without all of this, our nearest continent becomes somewhat more difficult to navigate safely or smoothly. The benefits that EU members get from membership is worth alot to the UK9.
Access to free emergency health care4 via the European Health Insurance Card. "EU membership... gives UK citizens travelling in other European countries the right to access free or cheaper public healthcare"5. When Europeans use the UK's NHS, their governments pay (just like the UK government pays when Brits use healthcare services abroad)10 - in this sense, there is no such thing as 'health tourism' within the EU11. The deal is that EU citizens pay local prices for healthcare, and countries cannot charge foreigners more. In other words, the EU's scheme on healthcare is good for all travellers, and is fair for all.12
50 million Brits travel to Europe every year1, and treating them in Europe "costs five times more than the equivalent cost to NHS"13 (saving the NHS money). And imagine if we had to pay the costs of the millions of Brits who have retired in the Mediterranean! The UK benefits from EU membership greatly in this regard.
Time and efficiency. The EHIC's ease-of-use saves time, and there's no requirement to organize health care cover on a country-by-country basis when travelling in the EU.
"Driving licences issued in the UK are valid throughout the EU"2. Membership of the EU facilitates harmonised motor insurance, motor insurance, vehicle registrations, number plates and other aspects of travel, and in each case, this saves individual time and expense7,8. Imagine having to go back to needing driving tests all over the place, and organizing car insurance on a country-by-country basis - not fun.
The Erasmus programme allows students to study for short periods of time in any EU country, providing a rich choice of valuable experiences for tens of thousands of UK students14. "The possibility to study abroad is considered positive by 84% of EU citizens"15. The programme has replaced and massively simplified a historical mesh of inter-country agreements with a single framework.