I want to fly from SFO to LHR this month, and I noticed that BMI has a UA codeshare flight from SFO to LHR in the W fare bucket for $683. This is several hundred cheaper than the UA fare without the codeshare. My question is this: Would a W fare bought on a BMI codeshare translate into the W fare bucket for UA? I'd like to use an SWU on this route.

Thanks