Private Tour Company

You don't need a tour company of any kind to visit Windsor Castle. Take the train, easy to do.

As Stratford upon Avon has a Shakespeare tour that visits all five of the historical Shakespeare sites that includes a tour, you just make you own way using the provided transport.

London Walks offers private tours to Windsor Castle. They mention that they can "arrange a private chauffeur."

https://www.walks.com/other-tours/private-walks/

Unless the elderly person in your party has severe mobility issues (other than just age) I don’t think you need a tour. The central station in Windsor is pretty much directly opposite the castle and a car couldn’t drop you much closer.

Thanks everyone. I know that we could do each of these as separate trips on different days from London, but we wanted to link them together and just make it easier for my father. I'll take your advice and look at trains. Thank you.

Oh my, I don't think doing both on the same day is a good idea!

For myself Windsor takes 3/4 a day. Haven't been to Stratford-upon-Avon in years so no idea how long that would take.

Does your Dad feel like he wants to see both? I'd probably choose Windsor as it's less of a fuss to get to.

It takes a FULL day to see Stratford upon Avon, doing the five sites with the Shakespeare tour and general covering the wonderful town.

By train it is effectively impossible to do both on the same day.
Even by tour bus or private driver you are pushing it.

Many thanks for the advice.

This is more of a related question than a new reply. My husband and I will be in the UK next month, with stays in London, the Lake District, and Northumberland. We probably will take a few guided tours in those areas as well as explore on our own. Particularly in the Lake District and Northumberland (based in Newcastle-upon-Tyne), we would be more likely to take tours since getting around without a car would be more challenging. Can anyone suggest reliable tour companies and/or specific tours in those areas? I've been doing research and already have information but would welcome suggestions from people with local knowledge.

@NJM-
In the Lake District getting around without a car is very easy, at least to destinations international tourists are going to be visiting. There are very good and comprehensive bus services in the Central Lake District.
However the main operator of tours in the Lake District is the Mountain Goat- https://www.mountain-goat.com/

I was only thinking today of how limited the itineraries of people on this forum are in the Lake District when I was reading of one of the County's more interesting tourist attractions opening for the year- just 4 miles from Keswick yet never visited by people on here or by tours (which suits us locals just fine).

Newcastle for Northumberland is a lot more challenging for tours as there are just not the international visitor numbers to justify operating them.
You will doubtless find tours to Hadrian's Wall, but not to the coast.
Domestic visitors either use their own cars or the good bus services. Many of those buses start from Newcastle. But a lot of the distance can be short cut by using the regular stopping train services between Newcastle and Berwick on Tweed calling at Morpeth, Alnmouth (for Alnwick) and Berwick. There are always short notice cheap Advance Fares available on the stopping trains.
It doesn't much matter who runs each train, but the services are provided by 5 train companies- LNER, Lumo (Morpeth only), Northern, Cross Country and Trans Pennine. Just buy tickets from any of those companies
Within Northumberland day rover bus tickets cost £6 per day, from Newcastle into Northumberland £7.50.