Table saws for cutting blanks - I think you will probably get more recommendations here for using a band saw than TS, but I will go with the TS. And that is what you asked about.
I have a BS and a TS and most of the time I prefer using my TS. I have a 10 inch TS and it is a fairly accurate precision saw. However, I made benchtop TS for cutting blanks from a quality circular saw.
http://www.penturners.org/forum/showthread.php?t=3838&highlight=Table
The problem with affordable job site TS is that most saws $300 and under are not meant for precision as much as job site and framing construction - in which cuts more precise than 1/32 are negligible.
I could be wrong, but it seems you are looking for the ability to make some precision and smooth cuts. That is the basis that I am writing from. :wink:
AS to blades, thin kerf and 48 to 52 tooth would be the minimum that I personally would consider.
Here are two quality hobby saws - that are expensive:
http://www.byrnesmodelmachines.com/tablesaw.html?id_mm=0524MM984673
http://www.woodcraft.com/family.aspx?FamilyId=4905
If you look for some "used" saws online, Ryobi made a couple of saws (now discontinued) called the BT3000 and 3100 that was known for its precision in light duty work and some in heavy duty work if taken very slowly. It is a bench top machine but had a stand also, weak in power by construction standards but fine for the take-your-time slow deliberate cuts. That machine is a little difficult for some people to set up and maintain, but if a person is good at tinkering and following instructions, that saw offers some precision cutting. I have one in the US (3100) and one (3000) in Japan. I am not totally easy on them, but they hold their settings well for me. I have registration equipment for checking accuracies and they stay that way for me. I use mine about once a week and have to adjust things (sliding miter table and fence) about every couple of years.
If this were not my TS for normal (flatwork) woodwork, I would gladly have tweaked it to be a blank cutter. On most 10 inch saws, you can substitute a 7 to 7 1/2 blade such as a Diablo that has 1/16 carbide kerf.
-> Just noticed that you are from England. May not be able to get a used BT3x00 there. There were sold there for a while though.