Chasing voters in Spain

Up until I read about it in the English press I did not believe it, but all the Brits abroad are being chased to vote at the next election, not only in Spain but Australia too.
Conservative Spanish branches are trying to persuade some of the hundreds of thousands of Britons resident in Spain to register as voters, emulating the efforts of the prominent US political groups.
In terms of numbers of British residents abroad, Spain lies fourth after Canada, Australia and the US. It is home to many Britons who maintain close ties with the UK, and Conservatives Abroad has more branches in Spain than anywhere else.
Spanish statistics show that just under 700,000 Britons have registered with the authorities as residents, although the real number is thought to be higher. Many UK pensioners live on the Mediterranean, especially on the Costa del Sol, the Costa Blanca and the Costa Brava.
I really do not know how this works, the Lady of the Villa and I are registered with HMRC as living abroad and registered in Spain as resident and able to vote. So can I vote in the UK and Spain? I will look into this