There are only two platforms with advantages over the Chinook:
The Sea King has a better door for winching, but then that is not a primary role and the Chinook has far better hover performance crosswind.
The Puma has a smaller footprint, a point noticed in the last few years and utilised to good effect overseas.
Other than that, the Chinook beats all comers hands down in every respect. So, we either need something small enough to offer an advantage in footprint, like the Puma offers presently, or just buy more Chinooks.
The Merlin is fine, but has a similar footprint with less capability in terms of lift capacity, begging the question, what's the point?
(Before anyone starts - you have a similar footprint to carry 22, instead of 44 which despite what Pegasus says, still happens occasionally, in all conditions)
NH90 is unproven, but could fit the bill.
Augusta, possibly and could gel nicely if it entered service with DHFS negating a long OCF and reducing lead-in times.