This issue is now resolved.

O2 are currently experiencing major data issues across the UK. This will affect Jump customers currently attached to O2 network because signal is still strong but there are data connection problems. We recommend manually selecting an alternative network until this is resolved if your device requires data.
O2 are continuing to work to resolve the on-going data issues. Customers using the Jump EU profile trying to move away from O2 network may also be experiencing issues when registering to the network due to the increased levels of signalling traffic being received from the O2 network. Telecom engineers are working to reduce the signalling traffic being received from O2.
Our network partners are receiving reports of wider signalling congestion within the UK network which is impacting both Jump UK & Jump EU SIM. O2 are still unable to provide a timescales for a resolution.
O2 have provided the following update - "One of our third party suppliers has identified a global software issue in their system which has impacted us. We believe other mobile operators around the world are also affected." We will provide further updates as and when received from O2.
We are seeing an increase in successful network registrations in the last few minutes, Engineers are continuing to actively monitor the network. O2 have advised that their software supplier continues to work to provide a permanent fix to the network issues.