1. Since 2008, the law in the US has allowed American citizens to hold dual nationality. This was granted by Barack Obama to placate the Jewish lobby most of whom held Israeli citizenship and so were precluded from becoming US nationals. Your first step is to apply for Indefinite Leave to Remain based on living in the UK for five years continuously. This can can then be followed one year later, by a UK citizenship application, based on having Indefinite Leave to Remain and being visa free for a period of one year.
2. Here is a link to the UK Government website which explains the requirements for Indefinite Leave to Remain or "Settlement" and guides you through the process https://www.gov.uk/settle-in-the-uk
3. Here is a link which explains the citizenship process for you https://www.gov.uk/becoming-a-british-citizen/check-if-you-can-apply. Be aware that you first need to jump the Indefinite Leave to Remain hurdle. However, it is best be aware of the requirements for citizenship from the outset.
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5. It sounds as if you need a different accountant! The key point from a tax viewpoint is that you don't have to automatically pay taxes in the UK on all your worldwide income, as you do with being a US citizen. Your tax liability in the UK IS BASED on residency in the UK and the remittance of foreign income to the UK. So, there is no automatic tax charge when you become a UK citizen.
6. Secondly, you will be able to apply immediately for Uk citizenship as you have been visa free in the UK since 1967. Applying as the spouse of a British citizen is the simple and easiest approach. You have already completed the necessary years in the UK for this application.
7. You will need to ask an American lawyer as to what are the disadvantages of gaining dual nationality from an american perspective. I can only advise you on UK law. So, I would suggest you file an additional question on the American end of this website for an Immigration lawyer as to the disadvantages of obtaining dual UK/US citizenship.