1) UK returns are Apr-Apr. You may file for 05/06 year end for any refund of PAYE withheld. The site is
www.hmrc.gov.uk. Unlike the US, you do not have to file if you do not owe any money and are not expecting a refund; provided of course that they did not request you file.
2) US returns are required Jan-Dec. You should file either August 2006 or January 2007 since you moved to the UK. There is a special extension to allow you to file late at
http://www.irs.gov/pub/irs-pdf/f2350.pdf. You are taxed on your worldwide income. While you must report your income in the UK, you can exempt it from tax using Form 2555. Thus, your US return is harder than before. Since your income in the UK is less than $80,000 per year, you may wish to use a cheaper option for tax-prep, such as a US-based tax-prep firm. Get a second opinion if (a) they say you owe tax, (b) they do not include your UK income, or (c) they do not include Forms 2555 or 1116 or both. You should consider getting international tax advice as your financial circumstances get better, as you do not want to expose yourself to a lot of unnecessary excess US & UK tax.
3) The bank report is Form TD F 90-22.1. You must file this form for each year you have access to a non-US bank account or securities account where the balances ever exceeded $10,000 at any point during the year. Access includes (a) your own account, (b) joint accounts, and (c) accounts over which you have signature authority, but do not necessarily own the underlying assets - such as a minor's account, an elderly relative's account, an account at your place of employment, or an account through a charity such as a church. It's available at
http://www.irs.gov/pub/irs-pdf/f9022-1.pdf.