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That is the correct family, but Frederick was born in Devon. I have a copy of his birth cert. Also I believe Florence was Amelia's 2nd name, which she use at times. In reference to Lily she is yet another 'problem' as I am only 80% sure she is Amelia's daughter. There is a possibility that she is Florence's daughter to Robert Murton. Which is why at the moment I am concentrating solely on Frederick. 

I have brought up this problem of mine before but rather than go though it to arrive back here I will start afresh armed with the new info as little as that is. I am looking to find more info ( census, marriage, death, etc) on Frederick Thomas Smith b 25 Aug 18 East Stonehouse Devon.  Residence 17 June 1889 London (ref school admission) 1891 Census 26 College St Southwark London. Parents Thomas Henry Smith mother Amelia Hexter. Amelia, later after divorce/death/separation from Henry changed her surname to Smythe around 1900 and so did two of her other children so it maybe that Frederick also changed to Smythe. My problem? I can't find him after the 1891 census. Any ideas?
I am also looking for his younger brother Charles William Smith but I will save that for another time.

That was supposed to be 'appear'

Just to add to the 1901 Census. Listed at the house is also Robert Murton a boarder from Folkestone. The enumerator noted below him Lily (Lilian) Smith age 3 born in Folkestone.
( relationship to head crossed out) The only other mention of Folkestone was made by Lilian on her 100 birthday where she noted she was born in Folkestone.  This is where my whole need to confirm Thomas's death comes in.
At this stage I am leaning towards Robert Murton being the father and either Florence Amelia or her daughter Florence the mother.  Something I don't think I will ever be able to prove.
I have not been able to find a birth certificate for Lilian and I know the requirement was bypassed when she received her message from the Queen on her 100th.
Florence Amelia changed her name to Smythe around 1904/5. All marriage certificates of her children that I have been able to find noted their father, Thomas was an Accountant he was noted as thus on the baptism record for Lilian as well. That was a lie he never was an accountant.

Head of household living in Tunbridge Wells Kent.