Yes but the Velvets are still psychedelic to some extent. All Tomorrows Parties certainly fits the bill with Lou Reed’s Indian guitar solo. Their first drummer had spent a couple years in India in the early sixties. Also they were doing some LSD. John Cale was apparently dealing acid in 1966. Brian Jones grabbed off him one time while in NYC.
Herman's Hermits - Gary Lewis & the Playboys The Dave Clark 5 - Paul Revere & the Raiders The Animals - The Doors
The Velvets are extremely psychedelic, assuming of course 'psychedelic' means more than having a very specific and dated sound.
Ramones - Sex Pistols (even Joey once commented he considered those two the stones and beatles of punk rock).
England - Cathedral Released one album only in 1977 (Garden Shed) and 1978 (Stained Glass Stories), that are both incredibly Mellotron heavy and now sought after on the collector's market.
I think Buffalo Springfield could be compared to Cream in the sense that they both were kind of supergroups and short-lived bands with strong individuals.
Of course when the Springfield got together there weren't well known and the members of cream already had big reputations.