I have done a bit of digging of census records and BMD records on the Ancestry and FindMyPast sites.
I can't find any likely Thomas with parents Joseph and Mary. I have found bits of information about a possible Birmingham family which MAY provide useful pointers, I'll list these below, and in subsequent messages.
The first question has to be: What is the SOURCE for the parents names JOSEPH CLIFT and MARY BLICK?Have you found a marriage record for Thomas in the US, as possibly this listed parents?Likewise the 'Birmingham' suggestion - WHERE does that come from?
I think you need to get the data from the US a bit clearer, as if the 'parents/Birmingham' info has come from someone clutching at straws in the UK, we may be barking up the wrong tree completely.
However, in case they give you some things to think about; here are a few bits and pieces. Nothing conclusive.
1) The Thomas Clift 1959 birth registration (as given in another posting): Births Jun 1859 CLIFT Thomas Birmingham Vol 6d Page 133 Please note that Jun means the Apr-Jun quarter. It is possible that a child born in March might not be registered until April, so would be indexed as being in the 'Jun' quarter. If you want to get a copy of this birth certificate to check parents, see: https://www.gov.uk/order-copy-birth-death-marriage-certificate. Note, however, that there is a death record in the same registration district for a Thomas Clift in the Dec quarter of 1959. As no age is given in the index, there is no way of telling whether this might be the same child, or a completely different individual. Name: CLIFT, Thomas Registration district: BirminghamCounty: Warwickshire Year of registration: 1859Quarter of registration: Oct-Nov-Dec Volume no: 6DPage no: 81
2) I can't find a marriage for a Joseph Clift and Mary BLICK, but there is a Joseph who MIGHT have married a Mary BLAKE in 1840.Several couples are listed per page, and the FindMyPast Index listed them all, not as couples.
Name: CLIFT, Joseph Registration district: Birmingham County: Warwickshire Year of registration: 1840 Quarter of registration: Oct-Nov-Dec Volume no: 16Page no: 460 Joseph Clift married one of the following people BLAKE, Mary CLAYFIELD, Mary Ann PADLEY, Sophia RADFORD, Elizabeth
This marriage doesn't seem to be on any of the other databases, so again you can only be certain by obtaining the marriage certificate.