As suggested by danuslave, a copy of the birth cert would certainly solve the problem.
In the meantime, the 1901 and 1881 census indexes suggests in 1866 Anfled (nee Ayling) Simmonds of Littlehampton married Philip A Simmonds (sometimes indexed as Alfred, who died 1911). They had five sons including a Montague (b c1876) who was still with the family in 1901. Presumably the father of your Archibald was one of those five.
The family appear on the 1881 census in East Preston as follows.
Head Simmonds P A 1847 of Folkestone. wife Simmonds A 1842 of Littlehampton.
Children: Harry 1868, Arthur W 1870, Walter G 1871, Ada 1874, Alfred M 1876, Philip P 1880.
An Anthony S------- on Genes Reunited seems to have researched this family extensively.
Roy G