In electronic terms UK Government is already very highly networked. However, this has had remarkably little impact on organisational structures within government, either in terms of management style or in terms of which remits are covered by which departments. Furthermore, despite hype to the contrary, this is unlikely to change.
Structures within government organisations are determined primarily by connections between issues (i.e. education & skills, work & pensions). Beyond this, management structures are determined by the need to deliver complex, manpower hungry projects with high levels of accountability. This virtually forces heirarchical management systems on anything larger than units of a dozen people. So long as we expect accoutability from our governments, it is hard to see how technology will radically affect these power relations and chains of accountablity. This is not to say that working practices will be static - they will - but the 'free working' civil servant is still going to to have to report up the chain to a minister, and the basic structure is likely to survive a good while yet.
However, just because technology looks unlikely to make radical internal structural changes doesn't for a moment mean that it can't make government look very different from the outside.