Yes, this is very unfair, it is also unfair that he very rich get heating allowance, as do those living in sunny climes. The only real solution is means testing which isn't popular politically but I think it must happen.
Either you spread the funding thinly between everyone, or you give a bit more and focus on those who need it, as long as someone is prepared to say who deserves it, and who doesn't.
The other side of the coin though is that if money is only paid out to those with no savings or assets, then the incentive is not there to save and build up assets for later in life, so more people then become dependent on the state. I think its an area that definitely needs looking at, but there are no easy answers, so politicians demote it to the back-boiler.