Where can I go to sit in the cockpit of a Boeing? This might sound like a silly question to some, but is it possible to go and sit in the cockpit of a Boeing 737, somewhere in the UK? (Otherwise in Europe, or beyond).

Maybe at a museum or something? I'm building a [currently tiny] home cockpit based on a 737, and I'd like to see how the real thing looks and feels.

I tried searching online, but I couldn't find anything.

Hope this isn't too dumb of a question, i.e. "not possible Jim!"
There is a company called Flight Experience which builds 737 simulators and offers their use to the public. These are fully certified simulators and are frequently used by commercial pilots for currency training.

Their closest location to London appears to be in Paris.

I had an opportunity to fly one of their simulators a few years ago, and it was a lot of fun. We spent some time doing landings at the old Kai Tak airport in Hong Kong.