When taking about open data or open access web services, even more important that the software stack being Open Source is that the interfaces are based on open standards. In the case of GIS those standards are developed by the Open Geospatial Consortium, W3C, OASIS etc.
There should be no problem communicating between web services provided by ESRI and the ones by OS Geo if they both follow the same OGC standards.
Ilkka Rinne