There is no issue with ROF and separate loaded ammo like 127mm. The Mk 45 loads at 20 rpm with electric fusing/ no fusing (16 rpm with mechanical fusing) and the Mk 8 26 rpm and 20 rpm with mechanical fusing. But that is simply the way the power loading system was designed separate loaded rounds carry both elements together and sequentially ram them split seconds apart. The Otobreda can load at 40 rpm and the Mk 65 48 rpm all with separate loaded 127mm. If you really want ROF then the twin barrel 127mm Mk 66 can load at 96 rpm.Apart from that, getting back to bigger guns, If the UK were to opt for say, the US MK45 - 5" Gun, then there would still be issues over things like buying a new ammunition type, all the spares, not to mention things like reduce Rate Of Fire (compared to the 4.5") & the 'double load', that's needed for the MK45, due to the seperate warhead & explosive.
Obviously replacing the Mk 8 with a new gun type is going to generate costs. But savings will be on hand via access to wider sources and supply lines of ammunition for either 127mm or 155mm. The clear advantage of 127mm is you can get it from any US, Dutch, Australian, Japanese, Spanish, Italian, German, Danish, Korean and Turkish resupply ship whereas 113mm is only available from British and Brazilian resupply and 155mm from land based Army stocks. Then of course you have the advantage of the wider number of ammunition types for 127mm and 155mm including a range of precision guided shells.
127mm shells can be carried by a two person cradle like 155mm....& finally, there are other issues to be considered, such as new legislation that will affect any NEW design / build RN warship, sincluding HSE rules about how heavy a weight an individual can carry (which I believe to be 25Kg, according to EU Directives), not to mention trade controls & rules about things like ITAR....