Will a non-EU citizen get stamped with a family permit at the airport?

EU law, specifically article 5(4) of directive 2004/38/EC, provides that

Where a Union citizen, or a family member who is not a national of a Member State, does not have […] the necessary visas, the Member State concerned shall, before turning them back, give such persons every reasonable opportunity […] or to corroborate or prove by other means that they are covered by the right of free movement and residence.

In other words, unlike anybody else who requires a visa, the spouse of an EU citizen should at least get the chance to prove they have the right to enter even if they did not complete the required formalities beforehand.

That said, note that:

• This is not the regular procedure, if the spouse of an EU citizen needs a visa to enter an EU country, they should in principle apply for it in advance (and that's definitely what I'd personally recommend). I would in any case expect some push-back and delays, which could be very unpleasant, even if you eventually get in.

• You still need to prove you are indeed the spouse of an EU citizen so have documentation to that effect (proof of your marriage?)

• I have no idea how well this works in practice. The UK has historically been rather reluctant to implement some of the provisions of the freedom of movement directive. For example, it took a court case and several years to force it to let EU family members with a residence permit from another EU country without enter without visa, something article 5(3) states unambiguously.

• Getting to the border might not be trivial. Airlines will for example want to see a proper visa before letting you board a UK-bound plane and probably won't take chances based on little-known provisions of the EU freedom of movement directive.

• I think you can use the EU passport lane if you are travelling together (definitely the case in the Schengen area, I think it's the same in the UK but I am not 100% certain).

In summary: EU law suggests it might be possible but the UK is probably the last country where I would want to try this. Don't do this unless you have absolutely no other choice. But if you do, it might still work, which is better than what most other third-country nationals could expect in this situation.