I am not sure that asking whether the exams are ‘hard’ is the right question. Westminster is a very academic school so they will be looking for pupils who will fit comfortably into the classroom. However I think they are looking for more. Not getting in does not mean you are not clever enough.
There are about 70 new sixth form places. There are a huge number of applicants, both in the UK and overseas. About 10 will probably go to boys, a third are ear-marked for boarders, and Westminster will want a spread of girls across subjects and across co-curricula activities (music, drama - they need that female lead!, sport, debating, school leadership). It would be easy for them to fill the places with super clever girls, but being cynical I don’t think it would do the boys egos much good if the top maths set was entirely female.
They also need girls who can hit the ground running and who they think will adapt quickly to a co-ed environment. Clever boys can be cocky, and to some, intimidating. Though in fairness most were welcoming - indeed having clever hard-working girls in the classroom was often quite a shock for the boys as well. UCAS and US University references need to be drafted in the summer term of Yr 12, so girls have to make their mark quite quickly.
When DD got a place some of the Paulinas she knew could not hide their amazement. Apparently the ‘cleverest’ girl in that year at SPGS had been rejected. Clearly DD was not nearly as clever. 
That said it is a fabulous school and it is worth having a go. DD enjoyed the process. The exams had a maths challenge feel. Not what you know but how you applied it. And the interviews were friendly and encouraged engagement. She was initially wait listed, so disappointed, but proud of how well she had done. I don’t know about others, but she did no special preparation. It meant she had to opt for a relatively hard question in one exam because she had not covered the other topic, but got to explain this at interview.