James Purdey and sons, Holland and Holland, William Evans will, I expect all sell you a lovely over and under double rifle. Once went into William Evans on St. James's St, near The Mall as I was in the neighbourhood as one of my sons was getting his Duke of Edinburgh gold award at St. James's Palace. Bloody lovely stuff in there. I bought a horn dog whistle. I asked to blow it before I bought it. It was about the only thing I could afford there, but it must be okay as I still use it.
To be honest, I think there's any number of reasonable gun shops if you venture a short distance out of London into the surrounding counties, which I would think would be a better bet.