Well Germany was first into space, with the A4/V2 missile, which met the altitude requirements (and at Mach 5 was also the first self-propelled vehicle through the sound barrier I think - self-launched unlike the X1, but not level flight and not manned). Obviously this was not orbital, but Von Braun intended to develop the A9 suborbital skip glider, then an orbital vehicle. This should be taken seriously, since this early work was the technical ancestor of both the Russian and the USAian space programmes.

The nearest thing to a second contender in early years would be the British IRBM development which lead to the one-off Prospero satellite. The same same rocket was used as the first stage of the ELDO European launcher, but that venture collapsed after ten failures of the unrelated upper stages. Later the descendant European Space Agency developed the Ariane launchers, without British participation for a long time.