Good Question. That old fart Robert Mugabe really needs to go.
I'd start by offering neighbouring Mozambique free aid for an unspecified number of years and cancelling its debt to the UK in return for basing rights and the use of its territory to land troops.
The Zimbabwe (ridiculous name) Armed Forces should give up when they see the might of the RN and Royal Marines headed their way. The Zimbabwean SOF, N Korean trained 5th Brigade and Presidential Guard might offer resistance-although I highly doubt they have the stomach for a sustained engagement-especially with a Networked force backed by Carrier Support in the form of F-35B/Cs. Hopefully the Brits can get some ex Rhodesian SOF from the Bush War to give them a hand because the UK was responsible for putting that fag Mugabe in power anyway and the people of Rhodesia deserve better after 20+ years of tyranny.
There are a few problems with this scenario. For example, by the time we have F-35B in service (BTW, we aren't getting F-35C), Mugabe will probably have died of old age, & any ex-Rhodesian SOF will be getting on a bit. The youngest will be pushing 60, & those with much experience will all be over 60.
I think the plea is for something to happen rather sooner than that, preferably this decade.
There is one sound point, though, which is that any invasion could take place through Mozambique. Transport links are poorer than from South Africa, but distances from the nearest ports are less, & the land border is much longer.
Izzy is right about the forces (& the colonialism bit), though. We're over-committed at the moment. Naval support would be no problem, we have the combat aircraft, & we should be able to scrape up the ground forces for a quick operation (though they'd be desperately short of helicopters, which would be a major handicap), but we wouldn't be able to keep enough troops in place afterwards to give a good chance of a decent handover to the successor government. I'd rather not be part of a half-done job. Not wise to repeat the initial mistakes in Afghanistan & Iraq.