The first stretch of the M1 opened in late 1959, although the short Preston Bypass in the north was the first road to be classified as a motorway the year before.
As Dennis says, there were indeed no speed limits on motorways in those early days, making the relatively deserted runs of motorway a favorite of the "ton up boys" of the early 1960s (so named for "doing the ton," i.e. hitting 100 mph).
The 70-mph limit was introduced on a trial basis in 1965, and made permanent a couple of years later. That's been the limit on British motorways ever since, except for a short-lived, temporary 50 limit imposed during the oil crisis of 1973.
The 30 mph limit in built-up areas dates back to 1934, but there was no general maximum speed limit on the open road. You can see the legacy in the sign which signifies "national speed limit," as it once indicated "end of speed restriction."
It was in the latter part of the 1970s that the maximum limits finally settled on the present values of 30 in built-up areas, 60 on two-way open roads, 70 on dual carriageways (divided highways), all unless posted otherwise of course.
http://www.highwaycode.gov.uk/09.htm#103If you look at the history of speed limits in the U.S., back in the 1940s a good few states didn't specify an absolute maximum outside of cities, just that speed should be "reasonable & prudent" for the conditions. Montana and Nevada were the only two states still having no specific upper limit before the nationwide 55 came along in the early 1970s.