Following a suggestion by Chris Wells, I've set out here how I went about researching "16 Cloudesley Square A House Through Time", which may be helpful to others.  I didn’t set out with any particular methodology in mind, but in hindsight this is more or less how I did it.

Start by using an Excel "work-in-progress" spreadsheet as a way of recording everything as you go along - see here for the one I used - make sure you have a nice big “Comments” cell against each name and fill it up with each new fact and reference as you come across it without worrying too much about style or structure. Then:

1. Use census results for finding individuals 1841-1911 – this is easy if you live in Cloudesley Square or Stonefield St - thanks to Jenny Tatton all the data is already on the Cloudesley Association website, here, and it’s quite rich.
2. Use Poor Rate Books at Islington Local History Centre (ILHC) for pre-1841 (a bit less informative since no data about families, lodgers, occupations etc) supplemented in my case with Cathy Ross’s excellent “Cloudesley: 500 Years in Islington” for insights into how the houses in Cloudesley Square were built in the first place – this will work for any houses on the Cloudesley Estate, but for areas further afield you will have to search out other histories of the local area, or piece it together.
3. Use Electoral Registers at ILHC for post 1911 - these are a bit patchy - lots of years seem to be missing, and the information is less rich than the census data, but it’s very effective for getting at least the names of those occupants eligible to vote. This can be supplemented with the Holy Trinity Births (to 1917) and Marriages (to 1932) data already on the Cloudesley website.
4. Having now got a list of all occupants at least every 10 years or so, I used mainly Ancestry (which you need to sign up for, and it costs money!) to look at each one in turn.  Other genealogy sites may be just as good.  This is probably the most difficult part of the research and is a bit hit and miss. Several names had no information or very little on Ancestry, but occasionally you strike gold.  Note that some of the information may not be accurate and using Ancestry is itself rather an acquired art – I’m not sure I’ve mastered it yet. A tip – make sure you document everything you find out immediately as you go through, otherwise you’ll find yourself having to go back all the time.

Throughout the process I also relied a lot on old fashioned serendipity – using the Internet to Google things I wasn’t sure about, which often resulted in new lines of enquiry. Balanced against this you need to have a laser-like focus or you’ll find yourself straying widely off the true path!

Images mainly came from Ancestry, ILHC, the Internet, and what is already on the website. You will need to seek copyright permission for all images used and I'd advise tackling this as you go along and recording carefully where you found each of the images.

Hope this helps,   Nick