Tickettyboo, JenB and Stan, thank you so much for looking at my query, it is very kind and I really appreciate it.
I came to the same conclusion as you last year and wasted my money purchasing a death certificate for Q2 1908 Thomas Anderson, age 77, Easington District. At least it helped me to prove that he wasn't my Thomas :-D
I've searched for Thomas everywhere I can think of and the next place left to look is in Jane's grave.
I've searched the newspapers on FindmyPast, the GRO indexes, Durham Records online, Probate Indexes, Emmigration records and the 1911 Census records.
Jane and Thomas still had their son George living with them on the 1901 census, he was single, aged 26 and a brick layer born in Murton. I can't find any trace of him either after 1901, I've also looked in military records and on his sibling's census records.
George is mentioned in his brother John's army records as being one of his full blood brothers, the information was completed by John's widow in 1920, it said George would have been 41 but his whereabouts weren't known, it also said that his parents Thomas and Jane were both dead.
I've found a burial record on Durham Records online for a Thomas ANDERSON buried in Murton Holy Trinity in 1908 born about 1836, the age is wrong but it could just be an error so I may send for the GRO death certificate if I don't find anything else.
I'm also going to write to the archives at Hartlepool Library that was on the link Stan sent to ask about the Grave records.
Thank you again