Firstly I was called up by someone at recruitment and asked some basic questions about my motivation for the role, why I applied and my background. They then explained the role in a bit more detail and said that they'd pass my details on.
I was then invited for a one-on-one interview in their London office. This lasted about 45 minutes and was quite simple. Basically just reviewing my CV, and asking me some classic competency questions, asking me to use the stuff in my CV as an example ("Tell me how you helped solve a difficult problem in your last job" etc.). I was also asked a logic question (how much water passes past one spot in the Thames in 24 hours) and was given ten minutes and some pencil and paper to estimate the answer.
I passed this stage of the application and was then offered a final interview (in London again) with 2 members of the consultant team (one new, one relatively senior) and was also told to prepare a 15-20 minute presentation on a "complex problem". I chose my dissertation topic from uni. They were polite and friendly, and during my presentation asked lots of questions. My presentation was about 10/12 minutes long and they commented afterwards that it was a little short so make sure to fill the time. The whole interview lasted about 90 minutes. They again asked me about my CV (in more detail this time), also asking me competency questions based around my extra curricular activities. They asked me how I would behave in certain scenarios (how would you give a technical presentation to a non-technical audience etc.). They also asked me about BAE, and wanted to know how much I knew about the business (what I thought the role entailed, what I thought Applied Intelligence did, what clients/competitors they had etc.), so make sure you do your research beforehand. They asked me about why I chose BAE specifically. The last 10 minutes of the interview involved them telling me more about the role, what kind of work I'd be doing and letting me ask any questions about it.
The HR team were quick with their correspondence at each stage, and informed me within a week that I hadn't got an offer. They offered me some feedback from both my interviews, where they said I didn't respond to prompts to offer more information about myself and didn't sell myself enough, so make sure you're not too humble/reserved.
