From the 1881 census, Arthur 'T' Perkins was a wine merchant, so was not necessarily in Ceylon for military reasons.
This is probably his family in 1861:
RG9/677 97/10
10 Anglers Street
(ink has become blurred a little, looks like, apologies for any mistranscription)
Fredrick Perkins, head, married, 34, Wine Merchant C?

?, b. Southampton
Isabella C. Perkins, wife, 26, b. Philadelphia America
Arthur F, 12, scholar b. Southampton
Rodney, 2, b. Southampton
Isabella, 8M, b. Southampton
there are visitors, servants, and two sisters in law:
Maud B.

?, 15, b. Cowes IOW
Cordelia Cr???, 13, b. Southampton
From 1881: Rodney has moved to York and is a dramatic actor, Frederick and Isabella Perkins are at a hotel in Kent - he's a 'Knight Merchant Ex MP'.! A Frederick Perkins (the same?) was the mayor of Southampton several times.
http://www.southampton.gov.uk/leisure/arts/sotonartgallery/search/view-artwork.asp?acc_num=601 - there's an image of Sir Frederick Perkins here.
Aha - my mistake, he was in the military:
The Times, Wednesday, Oct 31, 1866; pg. 7; Issue 25643; col A
Ceylon Rifle Regiment:
Arthur Frederick Perkins, from the Royal Military College, to be Ensign, without purchase, vice Tighe.
As for his birth:
Arthur Fred Perkins, Dec 1848 quarter, Southampton, Vol 7 page 218 is probably him.
- second marriage of his father:
The Times, Thursday, Jan 07, 1858; pg. 1; Issue 22884; col A
On the 5th, at St. Martin's Church, Trafalgar Square, Frederick, son of R. H. Perkins, Esq, Southampton, to Isabella Bloomfield, eldest daughter of J. H. Croskey, Esq, London.
Possibly the first wife was Evelina Abraham - a Frederick Perkins and Evelina Abraham were married 22 Dec 1847 in Portsea (IGI), and a Evelina Perkins died in Southampton in Dec 1848 quarter (freebmd).
From this, I can work out one of the sisters in law from 1861 also - Cordelia Burt Croskey, born 1847 Southampton, and Mary (not Maud!) Kelsall Croskey, married Henry Daniel Gooch in 1865 (Cordelia is living with Mary and her husband in 1871).