Ian, if you already have an FAA Certificate based on your UK licence, then you don't need to renew the Letter of Verification (unless you wish to add something else to the US certificate based on UK/EASA qualifications, which it doesn't sound as if you do).
However, if you wish to fly on that FAA Certificate, your UK licence must be valid - that is, your UK Revalidation or Renewal must be in date and signed up on the licence, all other currency requirements must be valid, and you must have a valid medical.
Having done the hours isn't enough if you are over the UK/EASA (not FAA) 2 year Revalidation by Experience period - you also need the signature from a UK/EASA Examiner on your licence.
If your UK licence isn't up to date and legal, then neither is your piggyback "61.75" FAA certificate, even if you have an up-to-date FAA "biennial".