You mention seeing a number of sites and that those travelling are older. This raises the question of how old - i.e. how mobile. Are there any mobilty issues etc?

Even if you had your own personal guide with you (which in my experience is something you don't normally see in London - other than for much larger groups), the question would still be how will you get about.

Quite simply, you don't drive between places and park up in central london. So, even if you had a guide they would need someone else with a minibus/people carrier ready to drop off and collect you at the exact time etc. (For larger tour groups, school trips etc, there will be a coach driver co-ordinated to arrive at right time, with arranged use of for coach bays, etc. Not practical for small groups.)

And you also mention being there for 4 days.

I'd seriously consider the hop-on-hop-off tour busess. They will drop you at the sites, you can spend as long at each as you want etc. I think some do tickets valid for a couple of days or 48 hours on the bus, so you could spread things out a bit. Or just do day one on the sight-seeing bus, and come back to some of the bits on your own.

If you are up to using public transport (e.g. the underground and the bus network), then I'd suggest you do that. The bus network is good, and frequent. And you can see a lot from the upper deck of normal bus, although you don't get the commentary of the sight seeing buses.
The tube network (underground) is also good and safe. Just keep in mind some lines are just below the surface others deeper - so don't make the tourist mistake of using the underground for everything, the map is diagramatic not geographic, some tourists go down underground, take a journey with a change of line, only to eventually appear again on the surface at a station that is only a couple of hundred meters away from where they started!