With visa matters, it's hard to say precisely how long things will take. One factor is how long the waiting list is for interviews at the US Consulate in London. As I understand it, everyone applying for a visa has to go to London for their interview, and that can take a while to schedule if you have to come in from some distance, stay overnight, etc.

The time table can also be affected by your personal situation - if your police record isn't squeaky clean, if you've traveled to "questionable" countries and have the stamps in your passport, etc.

There is also the matter of the US fiancé filing the petition supporting the visa application and if that runs into any issues.

The US State department makes no promises (and frankly dodges the question quite nicely on its website), but figure on at least a couple months, possibly more.
Cheers,
Bev