I hate moving, such a stressful thing to do, but i recommend AB removals, i've used them recently, reliable, polite and affordable. they are based in south west London and you can book them at short notice.
their website is www.abremovals.com
you can also get an instant quote on their website so you don't have to submit a form and wait for someone to call you back.
the price calculator link is http://abremovals.com/calculator/