Fleas are nothing to be ashamed of... but not sorting them out is!

They are a fact of life and as natural and common as a dog or a cat getting a dose of the 'squits' lol.
As Ambercat said, it is worth buying the more expensive treatments as they really
will work. Many times have I heard from neighbours, friends and other cat owners that they bought the pet shop stuff, but still had an issue and in the end have had no choice but to go to their vet and spend even more on top to solve the flea problem. That's worth thinking about during the current recession.
If you are not willing or able to buy a monthly spot-on treatment from a vet or pharmacist (we are talking Frontline from a pharmacy or pet shop, or other even more effective treatments like Stronghold, Advocate etc. from a vet which may also control ear mites and worms) then your most important outlay will have to be a huge can of Acclaim, Staykill or Skoosh.
The first two are well known to do the trick and do it beautifully; the other I haven't direct experience of, but - a vet nurse friend tells me in his opinion it may be less effective than the others. Treat your house with one of these sprays. Fleas do
not breed on the animals - you will never find flea eggs on your cat or dog, because the whole life cycle takes place in your carpet, curtains, nooks, crannies, sofa and curtains or even your bed if it gets that bad

And sometimes it can if left unattended!
Once the fleas have matured they jump on to any moving object (yes even people!) and take a nip. These sprays have enough in one can - expensive I know - to treat a average 4-bedroom house but normally go a lot further. And one application will last a year or more.
Your next armament in the flea war is up to you. Once the fleas are denied a place to breed you will see a huge drop in numbers. Now you have to decide how to control them on the animals themselves, if your dog or cat picks them up. There are herbal, holistic and homoeopathic methods available; or, if the recession is biting as much as the fleas *grin* buy some Frontline Spray. This is not available from chemists or online, but can be got from your vet, and it can be used on
both cats and dogs. Treat according to instructions whenever you see fleas, after making sure your home and the animals' quarters are up to date with home spray treatment.
Oops rambled a bit, but I hope it helps, it's my own way of tackling the issue and it's worked well for me for many years.
best regards!