Don't know if you got anywhere with this - but I would imagine it is highly unlikely that you would derive any benefit from keeping a track of your expenses.
The rent-a-room scheme is designed to be a flat simple scheme that does not allow expenses. I.e. you get the first £4250 tax tree and pay tax on the rest irrespective of how much you expend.
This is going up to £7500 next year.
If you thought that the amount you were spending on expenses (Mortgage Interest, Electrictity, Laundary etc) was likely to be more than this allowance then you would need to calculate your expenses and file a return. (Either way you may need to file a return but if you are just putting the amount of money that has come in on that form it will be very simple to work out.)
Essentially the key point is - whether to keep reciepts or not is not based on whether or not you take in more than the Rent-a-room allowence but whether you think you have more deductable expenses than that allowence.