The origins of EH101 go back at least to 1975. I joined in that year and studies had already been conducted on what was then termed MRFH - Multi Role Fleet Helicopter. This progressed to studies under the general banner of SKR - Sea King Replacement, including a significant amount of operational analysis of ASW operations. WG34 was a product of the SKR studies.
For reasons that are easy to understand, the aircraft was always intended to operate off existing frigates, which meant constraining the rotor diameter (and the folded dimensions of the aircraft) to be no larger than a Sea King. There were also demanding maximum weight, ship motion and wind velocity / turbulence requirements to be contended with.
These sorts of studies ultimately inform the Operational Requirements staff of what can be provided at acceptable risk / cost with the prevailing technology - in this case advanced composite rotor blades (both aerofoil sections, their distribution along the blade and tip shape) and modern gas turbine engines. It would be inappropriate to comment further on the operational requirements, other than to say that delivering the required missions implied a significantly higher weight than the Sea King, within a similar rotor diameter. You then have to look at power requirements and what engines are out there to come up with a viable design.
Suffice it to say that the design and the requirements ultimately converged between the UK and Italy. The early WG34 schemes reflect the fact that before determining the actual requirement, the customer needs to explore the boundaries of what can be achieved within particular constraints. A question to be explored might, for example, be what mission profile and time on station can I deliver within a certain weight, or if I am constrained to use two engines of a specifc type, etc. Studying the resultant configurations helps to bound the eventual requirement; it doesn't mean that the particular configuration being looked at at any point in time is actually a 'front runner'. You are in fact providing information to inform decisions and, in some cases, eliminate blind alleys.
Hope this is useful. I should stress that I personally had little involvement in WG34 as such, because I was looking at even more 'blue skies' projects.