Congratulations on going about finding a puppy the right way instead of just answering an ad in the free papers or online ad sites. Try this site
http://www.champdogs.co.uk/ click on guided search, then utility group, then lhasa apsos. there is then an option to limit the location, so press midlands and you will get a list of breeders. I would suggest you choose an Accredited Breeder, which means they adhere to the Kennel Club requirements/guidelines for health testing and breeding puppies. Make sure any parents are health tested.
Although you ask for 'cheap' puppies, there is usually an average going rate for each breed, and if you find a 'cheap' puppy it is likely to not be from health tested parents, i.e. you get what you pay for, and as you will hopefully have the dog for upwards of 10 - 12 years the initial outlay is very low considering the years you will have it. Another thing people often say they do not care about having 'papers' but this just plays into the hands of puppy farmers or backyard breeders, reputable breeders will know the pedigree of their breeding for generations and you should be able to see relatives and puppies from previous litters.
Have a look at some of the websites of breeders and see how proud they are of their stock.