You can chesk out Palmer Cleaners website - one of the biggest companies in London. You can ask for a quote on their website and get an idea of the prices.

For UK I can recommend - Andy removals. I've used them numeral times, my friends also used them and they did not disappointed even once. You can also check this article:  bucks.blogs.nytimes.com/2010/06/25/how-to-choose-a-mover/