Then, there is not only the EASA aerodrome certification to consider. There are also the issues of safety certification of air traffic management and air navigation systems, where mutual recognition is required, and no agreements will be in place if the UK leaves the EU without a deal. Thus, even if it was theoretically possible for EU-based aircraft to land at Heathrow, that is not practically possible without the use of air traffic management and air navigation systems.
On top of this, there are the wider issues of
open skies agreements and slot allocations, which also control commercial access to airports such as Heathrow.
Putting the fragmented areas together, it is very hard to see how, in the context of a "no deal" Brexit, aviation agreements with the EU can survive. There is bound to be a very substantial effect on European traffic and, because EU standards are linked with the US and others through bilateral agreements and working arrangements, transatlantic and Asian traffic may also be affected.
There is nothing, of course, that cannot be negotiated with the EU, but in the light of what appear to be deteriorating relations and with no Withdrawal Agreement in sight, the possibility of a "no deal" Brexit cannot be rules out. That would almost certainly bring international traffic at Heathrow (and all other UK airports) to a complete halt.
Getting the airport back in operation though would not be that simple. There is not one agreement to deal with, but a host of issues, including the highly technical safety issues, which require formal procedures to resolve. One would see pressure for emergency action but, if the EU stands its ground, it could be several months before full functionality is restored.
After such a break in operations, and the certainty that UK businesses will be
looking elsewhere, it would be unwise to expect traffic volumes be automatically restored. Reduced trade volumes will affect freight and business travellers, while uncertainty over visas and freedom of movement will undoubtedly affect tourism.