The British Library holds copies of a microfilm of Cecil manuscripts held at Hatfield House. This is accessible in the Manuscript Reading Room, if one knows to ask for it. The microfilm is old and not perfect, but for the moment, it is the most convenient way to access the Cecil mss. Unfortunately, finding the right manuscript facsimile in the microfilms can be a pain, as the HMC calendars and the manuscript volumes at Hatfield follow different orders.
There is, however, a guide to the microfilm, which matches manuscript volumes with microfilm reels. This is available in the reading room itself on paper, and online at the University of Hull State Papers Project website here. But I for one am thick enough to have been confused by this guide on occasion, and for that reason, I have created a quick search tool for finding the right microfilm reel. I have made this available on Google Documents here.
I'm sure there's a better way of doing this, and probably a way of making it accessible right here, but for the moment, follow the link..
Update 16.3.2011
So the moment I get around to creating the above tool (having been using the Cecil mf at BL over the past three or four years), I discover that the Cecil Papers digitisation project has finally been finished, and was launched by ProQuest in December last. The Cecil Papers (1540-1640) is a commercial product, like State Papers Online and Early English Books Online, but as the British Library subscribe to it, you would be more likely to use the Cecil Papers (Online) than the now completely-outdated microfilm. I have tried out the Cecil Papers (Online) and recommend it very much: the interface is clearer than that of some other similar resources, the search function is quite good, and the images are good quality colour photographs, which the user can also download as jpegs or pdfs (although you cannot do this at the BL).
Farewell, microfilm!
Note 10.1.2013
Most people who have used the Cecil Papers will have found that the foliation has some issues. I have tried to cover the intricacies of the foliation in a blog post here.
Comment 5.11.2013 (ed. 1.9.2020)
Although the digitised manuscripts are beautifully reproduced in the Cecil Papers (Online), there is still at least one reason why one might want to consult the manuscripts in microfilm as well as on CPOL. It would appear that the Cecil Papers went through cleaning and conservation between being microfilmed and being digitised, and in the process, some text has been lost. Namely, I know of a few cases where text clearly visible in the microfilmed images appears not to be there in the digitised versions of the manuscripts. In more than one manuscript, the removal of strips of paper which were used to bind letters has resulted in text written on these bindings having been lost (usually trivial things like parts of words from superscriptions/addresses). In some other manuscripts, marginal comments clear in the microfilm are very pale and difficult to see in the digitised colour photographs.