The first place you should look is Alison Games, Migration and the Origins of the English Atlantic World. She provides a thorough analysis of the 1635 list of emigrants leaving London to the English holdings abroad. She also gives a background to why the list was created and kept, I believe.

Other places to check would be the first volume of the Calendar of State Papers, Colonial found either here or here.

Then, move on to the index entries in the Calendar of Domestic State Papers, Volumes 1633-1634, 1634-1635, 1635, 1635-1636.

You might find some helpful updated discussion in Bailyn, Barbarous Years: The Peopling of British North America, but that tends to have a limited outlook, as the title suggests. A very thorough resource on Charles during the 1630s is Sharpe, The Personal Rule of Charles I, though I believe it is lighter on colonial policy.

Lastly, if you want to see the actual list of names obtained from the London Register of 1635, see Hotten, The Original Lists of Persons of Quality which is downloadable to pdf.