Thank you, @Peregrina651 and @Island2Dweller for your responses.
We will be staying in Central London for a few days post cruise, and I think have decided on a private car. I did fine Addison Lee, which seems reasonable and convenient but still trying to figure out the timing of things.
We'll be disembarking on Sunday, March 23rd. Since we initially had Viking Air, our guest statement has disembarkation listed as 6am, but no port arrival time. So I am assuming we will arrive sometime before that. I'll have to reach out to our travel agent to see if we can get an updated statement.