To fill in a tiny and not very important gap in Klepsie's excellent summary: Dot made one final and thrilling reappearance on the London label when the soundtrack LP of "Barefoot in the Park" was released here in July 1967 (HAD 8337), Not everyone knows that and even fewer care. It was a one-off: there were no other LP releases and no accompanying singles on London at that time.
First of all they were (usually) on London; then they moved briefly to Pye International (1964), before Pye gave the Dot label its own UK identity (for the first time) (1964-66); then there was a kind of interregnum until 1968 when Dot was relaunched in the UK as an EMI label (with the American Breed kicking off that series).
Ghod, where to begin ... The American Breed were signed to Dunwich Productions who supplied masters to Kenny Myers of Acta for release. Acta in turn had signed a deal with Dot for pressing / distribution .. the problem was that for about eighteen months Dot had no outlet in the UK, that's the period between the expiry of Dot's deal with UK Pye and EMIs launch of their Dot label in March 1968. They probably weren't all that interested as they were reorganising following the sale of U.S. Dot to Paramount.
While EMI was getting Dot set up they used Stateside to get "Bend Me, Shape Me" into the shops with subsequent releases on the group appearing on UK Dot."
I don't know exactly how CBS got involved with the "Step Out Of Your Mind " .. Dot effectively didn't exist in the UK in 1967 so Acta had to come up with some stop-gap deal to get the single issued. It's probable the CBS deal was at Dunwich's or Kenny Myers' instigation, I'm inclined to think it was Myers as Dunwich's inclination always seemed to be to concentrate on music and leave distribution / promotion in the hands of Atlantic or Acta or whoever else they were leasing masters.
What you have to take into account is that the early American Breed releases were the product of a series of interconnecting deals, deals in which the biggest player, Dot, was missing in action as far as the UK was concerned.
Looking at the world wide releases of "Bend Me .." is interesting, the Greek, Australian and South African issues are on Dot, the UK, Finland and Hong Kong on Stateside. I rather doubt the HK issue is from 1967, it uses the UK cat. number which would have originated from EMI in London so it's almost certainly from 1968.
It is probably worth mentioning that original US issuing label Acta was a subsidiary of Dot Records in USA, and at the time of issue through UK licencees EMI Records, they issued records from that source on the $tateside imprint.
Later records by the same group appeared on further EMI distributed UK imprints of Dot records, and later Paramount records, under their UK distribution deal.
The very first UK single issue by The American Breed was on CBS, but featured the name "Dunwich Productions", as did all their other UK output, although their first release in UK on Dot"Green Light" also mentioned that it was "An Acta Recording" .