A common problem I'm afraid when taking over an empty house previously occupied by a cat, the house had fleas that were feeding off the cat, now no cat so feeding off you.
You need to use professional pest control, such a shame you used Rentokill, they are the most expensive.
When I was doing pest control, I would have sprayed every inch of carpet in the house, that is essential! ( dont care what its says on the tin from the vet) I would then have used a smoke bomb (no not the ones you buy over the counter). The smoke bomb would kill every living flea within a few hours, the chemical sprayed on the carpets would take care of any eggs that hatch (the smoke has no affect on eggs and leaves no residue) If I was still trading now I would have charged in the region of £100 for a 3 bedroom house.
If Rentokill dont eradicate it on the second treament, go elsewhere and ensure you get a guaranteed treatment!
Fleas often need a second treatment I hasten to add.
Make sure that every inch of carpet is treated. make sure that you dont hoover for a few days after the treatment. When you do hoover, make sure you immediately empty the hoover out side or the fleas will find a way out again.
Good luck.