So, I went and did some research and while some countries do exempt their own citizens from extradition the US and the UK are not one of the ones those apply to. In the event that a country does block extradition of their own citizens they typically will try the person in their own courts instead. However while looking into this I found something else out about extradition I didn't know, which is that most extradition treaties require that the offense committed has to be a crime in both jurisdictions, so it wouldn't apply in this case anyway. There are also exemptions for "political crimes" although that's a rather vague term, and once again doesn't apply in this particular case. Lastly it seems like most extradition treaties only apply to crimes that carry a minimum 1 year jail sentence, so you're not getting extradited for littering or something like that.

The interesting bit I learned is that there are generally two kinds of extradition treaties. One kind lists a specific subset of crimes that the treaty applies to. In theory, you wouldn't need both countries to consider the act a crime in that case, as a country could request an extradition treaty for something the other country doesn't consider a crime, but the odds of the other country agreeing to such a treaty are pretty slim. The other kind of treaty is what most countries currently use which is an agreement that for things both countries consider to be a crime, if the offense occurred in another country then the accused will be extradited to that jurisdiction for prosecution.