Seeing as your William says he was born Glenfield on the 1871 census, I believe these records would be correct:
First: William Jarvis b. Glenfield Leics enlisted 1834 aged 18 years into 8 Battalion. Transferred to 1 Battalion in 1835.
http://discovery.nationalarchives.gov.uk/details/r/C12753528Second: Same man, in 1 Battalion, transferred to 5 Battalion in 1842:
http://discovery.nationalarchives.gov.uk/details/r/C11931278Third: William Jarvis of 5 Battalion discharged to pension in 1855:
http://discovery.nationalarchives.gov.uk/details/r/C12674338Son William appears to have been in 22 Brigade, here are the RA records of (some of?) his children:
http://discovery.nationalarchives.gov.uk/details/r/C11730153and his marriage:
http://discovery.nationalarchives.gov.uk/details/r/C11730056 The fact that the name "Lucambio" comes from the Basque region is interesting as in the 1830s, there were Royal Artillery detachments in northern Spain.
https://en.wikipedia.org/wiki/First_Carlist_War http://balagan.info/order-of-battle-for-the-british-auxiliary-legion-in-the-first-carlist-warAha! There is a child of the Jarvis family listed here:
http://dokuklik.snae.org/sacramentales.phpJust search "Jarvis" under "1er apellido".
Martina Luisa Jarvis Lujambio (first names, father's surname, mother's surname) was baptised 29 January 1840, Basílica de Santa María del Coro, Donostia.
Her father is listed as Guillelmo Jarvis Bonering (William Jarvis, mother "Bonering")
Her mother is listed as Juana Maria Lujambio Aldalur (Johanna Mary Lujambio, mother's surname Aldalur)
There is a possible baptism of a brother, Jose Manuel Lujambio Andalur in 1826, he seems to have died as Jose Manuel Lucambio Aldalur. This gives us possible parents for her - Angel Lujambio Alburena and Maria Josefa Andalur Cordova.
Angel Luxambio Albirena was baptised in 1790 as Juan Angel and died in 1844 as Angel Lujambio Albidena.
As you can see, you will need to be a bit flexible with spellings (use % as a wildcard on this search engine), but there is a lot of information there for you.