Hi , we live in an area where there is no gas too ! Your main options are a modern electric storage heating system , in a well insulated double glazed house the modern systems can be quite good , not as good as central heating , but not far off , although I have heard that a lot of electricty comanies have stopped offering economy 7 tarrif to new customer ( the tarrif where electricity is cheaper at night when your heaters are on ) , so it would be worth checking this out as it could make it expensive if you cant get economy 7 .
Solid fuel central heating , there are all sorts of systems that burn different fuels ( coal , wood , specialist fuel , multi - fuel ) although it does take some effort to keep it fuelled up and cleaning etc
and Electric central heating , this , as far as i am aware is fairly new and becoming more and more popular . I have heard it is very efficient and as good as gas , but you would have to look into it more closely .
Solar power is good for topping up your electric and lights etc can run on it but I dont think you could run a heating system on it to be honest . there is also ground source heating , where they use the heat underground to produce heat ..... very expensive to set up , but then low running costs .
Hope this helps a little