Pressuring the Union to give up slavery while trading with the slaveocrats in the South. Yeah, that totally doesn't undermine your anti-slavery position.
Actually, it somewhat does - they were trading with
both sides.
This is because Free Trade is seen as a good thing in and of itself.
Now, they respected (and didn't test) the blockade, which is actually in and of itself a concession
to the Union - the Union was insisting that they be granted legal blockade rights (which they got) while also insisting they were not a combatant because there was no war.
But when Confederate ships or Confederate private individuals showed up with money and purchased things, they were allowed to - because Free Trade was seen at the time as a positive good.
If the British had been
really, really neutral, or even pro-Confederacy neutral, they'd be aggressively sailing civilian ships through the blockade at the threadbare points and dates - those times the Union doesn't have enough frigates on station to catch them, since a blockade only has legal weight if the blockader can enforce it.