Out of interest, you say your original CU is full. What is the rating on the main switch of the CU, does it have a built in RCD and how old approx is it and are your current tails 16mm or 25mm.
It MAY be possible to offload a circuit (eg doorbell transformer) , onto another circuit (eg lighting) to free up a space on the cu , then put a mcb for the shower onto the cu, but obviously you need to make sure the main switch and tails can handle it (must be 25mm or greater), and main switch 100A , and RCD protection for the shower circuit is highly recomended, although its non statutory (You'd be silly not to have it RCD protected).
As regards to overloading, you MAY only have a house service fuse of 60A , and tails of 16mm, in that case, you need to contact the REC to upgrade the fuse and tails for you, as there is every chance of blowing the 60A fuse with that shower fitted. Ask them for an 80 or a 100Amp supply.
Best to check that first, because a 10.8kW shower will seriously load up your installation, whether you choose the seperate CU option or not.
______________________________
Post locked to stop more hi -jacking, not possible to "split" due to subject starting point