OP, your son can contact your local council. They will be able to tell you the total number of strays dealt with, of these how many were reunited with owners before going to kennels (ones who were chipped or wearing ID), of the ones who entered kennels, who were then reclaimed, and of the remainder, how many were killed and how many were rehomed/adopted. Most Councils will have figures going back for a number of years so you can map trends. As we are now in May, the total figures for the year 2010-11 will have just been compiled - years run from April to March.
Although this will not give you the total figure dealt with by all rescues, it will give your son a handle on the local authority's role and responsibilities. Some Councils will also have information about the stray dog service on the Council website, and it may also be worth your son having a chat with a dog warden who will be able to give a lot more detail.
Although big charities like RSPCA and Dogs Trust give lots of figures (see their websites for more details), smaller rescues are not obliged to provide any figures. If a rescue is a charity, then you can look them up on the Charity Commission website and see their income and expenditure which will be helpful in getting a feel for their work. Of course, not all rescues are charities and some are companies - Many Tears for instance which is a big organisation with a national presence. Slightly confusingly, this does not prevent them from asking for money/donations etc.
Also, bear in mind that rescues do not generally receive any money from either Councils or the Government, even though they may be preventing dogs from reaching the stray dog services run by Councils.
There is actually a big gap in the information on the numbers of dogs dealt with by rescues, and what makes it even more confusing of course is that not all dogs will be from the UK. Some rescues, Many Tears again for instance, regularly import shipments of dogs from Ireland. Some greyhound charities import dogs known as "galgos" from Spain (effectively Spanish greyhounds) because unfortunately they do not receive very good treatment there.
I'm seriously giving some thought to doing some proper research on this issue as it is sadly neglected at the moment, both by the practioners in the field and academics, although some aspects of dogs are being researched. There's enough material out there for several Ph.Ds and a whole journal of articles.
I currently work on stats for Wales - what I can get from local authorities, because FOI obliges them to provide it, but charities of course are under no obligation and in fact many are reluctant to discuss exact numbers for a whole host of reasons, some of them understandable.
How old is your son and what level is his research pitched at? He may be better off just focusing on local authority results which will be easily accessible.