Associate lateral move - pay cut

I am going to do a final round interview with a BB (GS, MS, JPM) for an associate role in London. I am currently at a boutique which has paid me, all in, in the last 12m more than what I would reasonably get paid at the BB (c. 20%). The base would go up slightly and the bonuses down materially. If I let them know that, will HR, in their infinite stupidity, or the team/MDs, see it negatively? Will they think that because they cannot match my current package they are better off by making an offer to someone else? Motivation concerns, etc.

I know it is an unusual question and the obvious answer is "just say the truth and tell them you like the job so much you don't mind taking a cut".

I am asking because I had a very odd rejection post-final round with a BB just after we started talking about compensation. I was the preferred candidate according to the headhunter and once we started talking about money they went silent and all I was told was they couldn't hire someone at my level and I think that by that they meant they couldn't match my comp. I told the MD and the headhunter that pay was not the reason why I wanted to move and a pay cut would be acceptable to me. I am not sure of the reasons for the rejection, I am just speculating.

Any real experience or proper insights? Should I massage the numbers?

I am not disclosing where I work and, obviously, I am not going to debate with the undergrad population in this forum why or why not I should go from boutique to BB and take a pay cut, so will ignore questions and comments around that.

Many thanks in advance for your thoughts on this.