There aren't enough private IPv4 addresses for large(ish) mobile networks to address all their customers devices. Some networks work around this by using public v4 addresses which simply aren't in use. The UK DOD's block has never been publicly advertised (AFAIK) so they decided it was a "safe" block to use for this purpose. This isn't a new practice - I remember seeing Sprint doing this same thing many years ago.
The "correct" way to handle this would be to reuse real private IPv4 addresses within your network by segmenting it somehow, or do what some networks have done (T-Mobile US is probably the biggest) - use IPv6 with NAT64. That lets them forego internal IPv4 entirely and only use it at the edge for NAT.
That's the best case scenario, considering that most customers probably don't need to connect to UK DOD. With the way IPv4 shortages are going, the more likely scenario is that some cloud provider/cdn buys that range, and sites start breaking randomly for customers.
I suspect major cloud providers may well end up buying the address space if it were to become available, so quite a few companies' services may not be reachable.
Most of these are routed and in very active use. I have suballocations of large chunks from 12/8 and 38/8. People will be unhappy if you picked most of them.
73/8 is entirely owned by Comcast and used for customers. 44 is no longer a /8, but sold+split and half in active use by AWS.
The "correct" way to handle this would be to reuse real private IPv4 addresses within your network by segmenting it somehow, or do what some networks have done (T-Mobile US is probably the biggest) - use IPv6 with NAT64. That lets them forego internal IPv4 entirely and only use it at the edge for NAT.