As others have said, it's a bigger deal for the US than the UK since the US consulting practice wasn't as far along the path to re-establishing itself. The UK seems to have taken a more organic approach, starting a couple of years ago.
This transaction may at least put the size of the consulting businesses in the two countries on a more level footing, although I expect there will be integration issues - couple a geographical split with a difference in legacy organisations and there will be significant barriers to people working cohesively, especially across the Atlantic. There are enough regional disconnections and inter-group rivalries within PwC already, so I expect the businesses will be blaming "cultural differences" for some years. If I was a multinational client, I would hesitate to see this as a panacea for the international client service problems that both Diamond and PwC have run into.
I'm sure the experience for existing clients will be handled professionally, and as smoothly as possible in the circumstances. Diamond's future has been in question for some time, so it may help assuage the concerns of clients on long-term transformation contracts that a large, reputable, business has acquired Diamond rather than it being broken up or folded. Overall though, I see this as a "sum of parts" deal rather than something that's going to generate a lot of additional value for clients.