Everything will the depend on what flying rights are granted after Brexit comes in to being. At the moment, it would appear that both the UK and the EU are envisaging that Open Skies will continue as now, and that means that a pilot (regardless of whether he is Spanish, British, an EU citizen or a non-EU citizen will be permitted to fly patterns as you describe.
The OpenSkies agreement allows EU and US/Canadian airlines to fly direct between airports in each other's territories, it does not allow US airlines to provide intra-EU flights between EU cities. If that were the case, the largest LoCo carrier in Europe now would probably be SouthWest airlines, not Ryanair. Also, it does not allow US pilots unfettered access to fly for EU airlines, or EU citizens to fly for US airlines.
Easyjet has established a company in Austria to enable it to continue providing intra-EU flights, which as a UK company, it would not be allowed to do after Brexit. Providing all its aircrew are EU citizens, it will be able to continue operating as before. The point of my post was, that as things stand at the moment, British pilots may be restricted to flying sectors where one of the destination/origin airports is in the UK.
Adding to all this uncertainty is the question of whether the UK will remain in EASA after Brexit and, if not, what are the implications. See link:
https://ec.europa.eu/transport/sites/tr ... safety.pdf
Another possible aviation problem that may arise after Brexit is whether flights from UK airports will still be allowed to overfly Russian territory in order to reach destinations in China, Japan, South Korea,etc. Airlines in EU member states currently enjoy Russian overflying rights under a EU/Russia agreement. For example, Finnair flies these routes as it is an EU member state whereas Russia does not permit Norwegian to do so as it is not a EU member state. Given the current frosty state of UK/Russian relations it would not surprise me if overflight rights for flights from UK airports are withdrawn post Brexit. This would require passengers from the UK to take a flight to a EU airport first to make a connection with flights to the Orient.