Beef tea is the Victorians answer to using up bits of beef as a healthy drink. If you have a Makro card or any good cash and carry for that matter (of know someone that can sign you in) go to the drinks aisle and get a tin of Bovril drink powder.
Makes a good beefy hot drink. The powder is just about the same as the 'paste' in a jar, so you cold use that if you fancy.
A broth is just a liquid in which meat bones, meat, fish, cereals or veg have been simmered - not boiled. Once ready, strain the liquor and -- ta da!...broth. Reduce this a bit for a 'fond brun' (brown stock) or use a base for a good gravy or soup stock.
For a cheap basic soup, try making an oxtail soup using the bones and the meat, strain off the fat that rises to the top of the pan and if you add a few pearl barley or some rice and small dice veg you have a lovely warming soup. Bit like a broth....
Recipes similar you might find are Brown Windsor soup, Scotch broth or a Welsh broth called cawl.
One to try:
http://www.thefoody.com/soups/scotchbroth.html