Intended travel date

How would you go about extending the 30 days, due to unforeseen circumstances we may have to delay the flight to the UK...

Any advice would be much appreciated.

As larrabee said, I would not delay entering the UK if you can possibly help it... it's a bit of a pain to get a visa with new dates to enter and it costs a couple of hundred pounds extra to do it.

If you absolutely cannot travel within the 30 days, you'll have to fill out an application form for a replacement 30-day vignette, pay $242 and mail your passport back to UKVI so they can replace it (not sure if you send it to Sheffield or New York though since the person larrabee reference sent hers to Sheffield and it was returned without being processed, with no explanation or advice about what to do next).

See:
https://www.gov.uk/government/publications/transferring-a-visa-to-a-new-passport-ecb17/transferring-a-visa-ecb17#ecb173-replacing-a-30-day-short-validity-travel-vignette

https://visa-fees.homeoffice.gov.uk/y/usa/usd/other/other-fees/vignette-transfertransfer-of-a-valid-visa-vignette-to-a-new-passport-or-replace-a-loststolen-document

https://www.gov.uk/transfer-visa