Inn to inn walking in the Dales or Peak District.

We've done several Contours Walking Holidays self-guded walking trips and been very satisfied.
https://www.contours.co.uk/walking-holidays/england-north.php

For a selected route,Contours does the booking, luggage transfer service and provides Maps, guidebooks and or walking instructions and general advice. You can usually select !ong or short walking days and add on layover days.

Our trips were all May trips. Comfortably cool with some hot days. Expect rain (and wind). It's England. Down side of October is shorter daylight hours than late spring/early summer. Some B&Be don't serve full breakfast as early as you may prefer.

If you plan on train travel to the north its a good half day plus depending on where to. For a pm LHR arrival plan on spending the night in London near the appropriate train station. It doesn't hurt to have a day or two in the event of delays or late gear.

Contours can/will advise on travel options to/from start of walk.

And if Contours does not have the itinerary you want, try Celtic Trails.

Thank you both for the advice. I am hoping for good weather.
So excited about the Plague village of Eyam.

It will be colder than southern England, but it's impossible to predict what the weather will be--you can get four seasons in a day. You'd best just be prepared for anything from an Indian summer to snow and see what turns up.

It is so hot and dry here in Texas, it all sounds good.
We will look into some rain pants and coats for walking.
Do umbrellas work or is the wind and rain strong?

Looking at "average" climate data, rain is a high likelihood in the Peak District:
https://www.contours.co.uk/weather/weather.php?rid=329

A "rain day" can be a gentle day of off and on drizzle (famale rain in Tony Hillerman terms) or a full on maelstrom where the rain comes in sideways. Breathable rainproof jacket with hood, rainpants gaiters and Gortetex lined boots are the uniform for those extreme days. The alternative is to hitch a ride with your luggage. I'm partial to Nickwax water repelling products.

I don't do umbrellas because of the wind and because I use trekking poles. Yet I saw a couple of Englishmen carrying umbrellas in their packs up Ben Nevis though it was a blue sky day and they don't need to deploy the umbrellas. If you try a poncho you need a belt (wind).

Pack covers or waterproof bags for pack contents are useful. Waterproof map cases are essential.

And bring shorts for those glorious blue sky warm days.

PS. Carry extra socks. No matter rain pants and gaiters my socks get soaking wet in heavy rain. Nice to change socks while drying off with a bowl of hot soup at the pub.

If you're doing all day hiking, I would bring a rain jacket and rain pants. Rain pants are good for more than just rain -- you can use them for wind and cold too. My son wore his rain pants this summer when he insisted on wearing shorts and then decided he was cold midway through the hike.

I actually like bringing an umbrella too. It won't work if is windy, but if you don't have wind, an umbrella plus rain jacket and rain pants will keep you dryer. You can also use an umbrella as protection from the sun.

The umbrella is probably optional but I think jackets and pants are essential.

It sounds like the consensus is prepare for windy rain and hope for a light rain and be thrilled if it is sunny.

Well, we are still excited about the trip and will prepare for the worst.

Perhaps there are taxis to get to the next accommodations if the weather is horrid and we cant walk.

At least there aren't tornados!