No idea about what is more expensive, I have never rented a flat in the UK, so I can't tell.

But something that always takes newcomers by surprise is how small flats, and housing in general, can be in London and the UK in general (there are no laws about minimum room sizes, like in Germany lets say).

I count several friends and acquaintances that had to put in storage half their belongings because they could simply not fit them on their new home.

I frankly would not bother bringing run of the mill furniture, you can get it on IKEA here, or buy it second hand on Ebay. Maybe you could consider buying something really nice and then bring it here to sell for a profit ;-)