Sounds like short termism to me. The Government needs to be looking to the longer term. People will be affected by the current economic crisis for some time to come so they will need to be supported. As for a windfall tax on energy companies? Could push the price of energy up even further. I also believe that the Government should have foreseen a potential economic slowdown on the horizon and should have saved accordingly so as not to have needed to impose a windfall tax in the first place.
A simple one off payment probably isn't going to make a huge difference in the long term. While a windfall tax sounds like a good idea it may be better to encourage investment by the power industries, especially as things like electricity generation are going to be hit shortly when power stations reach the end of their design life. However, perhaps it would be better if the government directly funded energy saving improvements to homes? Such as cavity wall insulation, more efficient heating etc? That would last longer than a single payment.