As with most things at BA, status and class of service flown really make a difference re getting their attention.

Over the holidays, we were on the first flight LHR-ARN, bags didn't make it during 3 hour stop at LHR. Although the bags arrived at ARN before noon, we didn't get a call from BA until 10 pm, stating that they would be delivered the following day. Whe I stated that I thought it would be better to have them this evening, via taxi, I was told it was not possible.

When I suggested that she check our details, her response was "we don't have many Gold members arriving in F from SYD...we'll get them right out to you". The bags were there in 45 minutes.

The morale: there's probably a lot of squeaky wheels ahead of you, thus the perceived lack of responsiveness. Not the whole problem, but might exacerbate your situation somewhat if you are a first time Ba flyer.