I'm presuming he is the Reginald A aged 1½ in Islington on the 1901 census? His birthplace looks to be Worthing which is in Sussex. The person above was born in Surrey but I don't think there is a ditto sign for Reginald below. I think that is a mistake on the part of the indexers.
On FreeBMD there is no birth registered for a Reginald A Blunden at the end of 1899 (or within a couple of years of that date - FreeBMD has full coverage of the civil index for this period). No registration of a Reginald Blunden at all.
What there is however is this birth registration which could of course be a coincidence.
Lyons, Arthur Reginald, December quarter 1899 Volume 2b pages 347 registration district East Preston Sussex.
East Preston registration district covered Worthing.
I have checked the civil registration for any subsequent death of this child before the 1901 census, and also the 1901 census for a child of a similar age born Sussex called either Reginald or Arthur Lyons and could not find one.
As I said it could be coincidental (the family could have emigrated) and you have no knowledge that your grandfather actually started life with the name Reginald (I don't know what the A stood for - did your grandfather have a middle name of Arthur?) just that his surname was Lyons. He could of course also had his first names changed as well as his surname.
Cecil Robert Blunden the head of the household on the 1901 census, though born in Sydenham Kent circa 1870, married Mary Ann nee Randall born Liphook Hampshire circa 1862, in East Preston registration district in 1890. On the 1891 census he and his wife and his younger brother were living in Broadwater near Worthing.
Does any of this look hopeful? If you think it does then it is worth the risk of purchasing the birth certificate. From the information contained in the birth certificate if might be possible to find the parent or parents named on the censuses and perhaps even work out what the connection to the Blundens was (though it might only be one of friendship). I would be happy to try the search for you if you do not have access to the censuses.
Regards
Valda