I think it's a good idea to have a look at the churchyards whilst you are here in the UK and keep a good record of any Thompson headstones that you find.
I have another spanner to drop in the works! There is a burial for a Robert Thompson on 19 January 1842 at Carlton in Cleveland aged 35. The image from the PR states "of Preston in the County of Durham."
Looking at the 1841 census there is a Robert Thompson age 30 M.S. (male servant) with presumably wife Mary 30, children John 8, Ann 7, Jane 6, Robert 4, Mary 2 (all have N. for where born) & William 3 m, has Y for where born. They are living at Preston Lodge, Preston in the Parish of Stockton on Tees, Durham.
GRO listing for birth of Mary could be M1839 Stockton & Sedgefield and for William J1841 Stockton & Sedgefield. Both have mother's maiden name of Wilkinson.
Marriage: At Whorlton on 13 Oct 1832 by Licence: Robert Thompson of Ingleby Greenhow & Mary Wilkinson of this parish. The Licence details give both ages as 21, but that could mean just that they were both of full age. Remember that "of" in a marriage entry just means that the person was living in that place at that time.
There's also another baptism in the vicinity - Robert Thompson 31 Aug 1806 at Faceby, son of John Thompson Junior farmer. (Robert & Mary's first child listed in 1841 above is John)
Faceby, Carlton & Whorlton are all very close. Ingleby Greenhow is about 6 or 7 miles away with Stokesley about midway.
In your first post you stated that Thomas was your 3 x gt grandfather ........ then his son Robert who married your 3 x gt grandmother Margery Jefferson. Which is correct? Is Robert your 3 x gt or 2 x gt? Perhaps go back to grandparents and great grandparents and take it from there. I had a Thompson brickwall in my tree for about 10 years but eventually got through to the other side! 
Perhaps you need to have another look at "your" Robert when you return home to your notes and go back to what you definitely know, backed up with certificates or parish register entries and then see where there are several Robert Thompsons who could fit the bill..... 
Thanks Tillypeg, apologies yes Robert is my 2 x GG and Thomas my 3 x GG, (stubby fingers and no proof reading). I have all info back home however used FindMyPast and Family Search to reconstruct it. Henry Edward Thompson is my GG (confirmed), he was born 13 August 1847 South Shields (christened 24 Oct 1847 St Hilda's church) to parents Robert & Margery Thompson. 1851 census has R & M Thompson living in Westoe, South Shields with their 10 children (the eldest Harriet is not there). Henry Edward is there but only indicated by his initials H E. Roberts birthplace is stated as Yorkshire however as previously mentioned future census have him as born Stokesley.
The marriage of Robert to Margery Jefferson took place on 12 Dec 1824 at St Paul's church in Jarrow (next to South Shields), however the bishops transcript has her as Mary not Margery, I presume a mistake when copying the original which was probably Marg. It's funny but FindMyPast has it as Dorothy Jefferson (how they got that I have no idea!!). A witness is Thomas Thompson.
So as you can see this brings me back to Robert Thompson, son of Thomas Thompson christened in Stokesley in 1810 but born in 1804 according to all the census and his death certificate, which is now where I get stuck. I has seen the other RT's that you have mentioned but have dismissed them as having nothing to do with South Shields.
Yes I will be taking photo's of all Thompson graves while I am down there. I have photo's of some Thompson families taken last time on my wanderings through the main S S cemetary, however have a larger list this time (branching out) to go and try to find there.
One of my biggest thrills last time was knowing that my GG the above mentioned Henry Edward and his wife Jane were buried in Gateshead's largest cemetary, but not knowing where (£30 per search to locate where) I decided to walk around, I think stumble is a better word, falling over hidden fallen gravestones, fighting with ivy growing on the gravestones and rolling an ancle on submerged pieces of grave. After about 4 hours almost having given up hope I stumbled upon it, it was one of the best feelings of my life. The grave hadn't been visited for many a year but was still in excellent condition and contained not only Henry and his wife but also the eldest daughter. I cleaned up the grave, pinched!!! a vase from a long forgotton grave that had 3 of them, went and bought some flowers and talked to them about their future generations. It seems silly talking to them but it felt right after finding them.
So that's where I'm up to, I still think I have the right Robert but as to his parents, I would say Thomas was his father but what else?
Many thanks, Paul
