As you are departing on a Sunday, the first direct Underground from the Kensington area doesn't get to Heathrow Central until 08:15 which will be an issue if your flight is before 10:00
In answer to your original question the current benchmarks for low cost budget hotel at Heathrow are the Ibis Heathrow and Travelodge Heathrow Central (room rates around 18-45 GBP).
You can either take a Hoppa Bus direct to these hotels from T3, 7 GBP return per person or you can walk to Heathrow's bus station and get the 105 or 111 local buses that are more frequent and run 24x7 which are 2.20 GBP each way or free for the Ibis.
Unlike a lot of Heathrow hotels both these hotels have alternative options outside the hotel for food/drink, especeially the Travelodge.
Edited: 20 February 2011, 9:20