ATG,
A very good example, even if the MoD is looking at a number greater than 4!
A small unique fleet is not viable as training, maintenance and development overheads would eliminate any realistic capability.
A cooperative program such as the original C-17 program can punch above its weight as the wider program can absorb the training, development, weapons and major maintenance overhead. Adopting a type from a larger production run can also allow the UK to be more selective in its spending profile. Finding the money to buy aircraft every so often is just not possible with a unique fleet off a dedicated production line.
A future conflict where the UK can contribute a small number of P8s to augment the exact same type operated by the US and Aus sounds quite attractive to the UK right now. Pitching up at the last minute and buying a bunch of the exact weapons needed for that particular scenario direct from the US Navy sounds attractive to those who hold the purse strings.
None of this will be easy given the mess we are in, but it is far from impossible.