As Greg Hewgill notes, you do not need a visa to enter the UK because you are a US citizen. For people who do normally require a visa, the Spanish residence permit will exempt them from that requirement.
In fact, that permit, which should be endorsed "family member of a citizen of the European Union" (or the equivalent in Spanish) is evidence of their right to freedom of movement under EU Directive 2004/38/EC when they are traveling with, or joining, their EU-citizen family member. One benefit of this is the right to use the EU passport lines (at Schengen borders, at least) even though you do not hold an EU passport.
For those who are from a country whose citizens require a visa to enter the UK, and who have not yet received a residence permit, or do not themselves reside in the EU, there is the EEA family permit. (For family of British citizens, this option is only available if the British citizen lives in another EU country.) The permit is free of charge.
See also http://europa.eu/youreurope/citizens/travel/entry-exit/non-eu-family/index_en.htm
With regard to the British citizenship question, you have to live in the UK for a minimum period before you can be naturalized. For spouses of British citizens, this period is reduced to three years from the usual five years.