Conservative Home has the full text of his letter here. It seems one of his prime motivations was David Cameron's fairly Euro sceptic stance.
David Cameron's reply is:
Dear Quentin,
Thank you for your letter. Your decision does not come as a surprise to me.
The Conservative Party has changed, as you say. We need to do more to protect the environment and tackle climate change. That will mean taking tough measures on carbon emissions. And it does mean looking at ways to encourage greater use of alternative sources of energy. Of course, I will also continue to stand up for Britain’s interests in Europe, and work to give the British people the referendum they were promised.
People see that we are now focusing on what matters to them. That is why so many people are supporting us once again – as shown in May, when we won over 900 Council seats.
I am sorry that you feel unable to be part of today’s Conservative Party, and join us in campaigning on what matters to people – for example, against the NHS cuts or for a better deal for pensioners. The big dividing line in British politics is between Labour’s approach of top down State control and the Conservative vision of pushing power outwards and downwards from central government, trusting people and sharing responsibility with them. You have made your choice and the British people will make theirs.
Thank you for your support in the past. We will watch your future career with interest.
Other reactions from this BBC article:
But Mr Hill said: "I think it's a slap in the face for all of those people who supported and went round for him.There are also rumours that he faced deselection in his constituency.
"I feel very strongly, I don't approve of politicians who stand under one flag and then change to another flag for their own convenience. It is an act of treachery and betrayal, frankly."
David Davis, the shadow home secretary, said he was "extremely surprised" at the news.
Sir Nicholas Winterton, Conservative MP for Macclesfield, called for Mr Davies to resign his seat, adding: "All I say is 'good riddance'."
Tory peer Lord Tebbit said: "This defection will raise the average standard of members on the Conservative side and lower it on the Labour side."
Shadow industry secretary Alan Duncan said Mr Davies was "not socially liberal" and against "a changed Conservative Party".
He added: "And basically he's quite grand and old fashioned, and I'm surprised that he finds that the Labour Party will offer him a happy home for those attitudes."
Nick Robinson has an interesting piece on his blog here. Iain Dale also has this interesting article here, and what Quentin thought of Gordon Brown today and last year!
Update:
I forgot to hat tip Rik W on politicalbetting.com for the text of Cameron's letter.



