I think the simplest answer is that I have found nothing definitive. However, on the balance of probability, I believe that the William Beck, that fathered William Richard, was baptised at Chard, Somerset on 14 April 1811. He was the son of Richard and Betty (nee Palfrey) Beck.
William Beck married Mary Moles on 18 July 1829 at St Helier, when he was said to be of the Parish of Charge (Chard) Somerset. Apart from this marriage all I have been able to find is two baptisms where William is noted to be a Shoemaker. I have not found any baptism for a Thomas although that doesn't mean one does not exist. I have not found any death nor census returns!
Apart from the clear link to Chard, the Beck Family has a history of Shoemakers, including in all likelihood William's elder brother Richard.
There is also a Will of a Samuel Palfrey (father to a Betty) who was a Shoemaker of Chard.
So, as I say nothing to be 100% on but, some good circumstantial evidence.
Best wishes,
Tony