I am no expert on this part of Mexico, but cannot believe there are no hotels for under 250GBP.

See this.
https://www.fodors.com/community/mex...otels-1732724/

I’m currently in Oaxaca, a week into a planned 5 month stay. I was last here 8 years ago and because of circumstances this time was unable to book accommodations in advance. I found a place for the first 6 weeks and was unconcerned about filling out the calendar until I started seriously looking after arrival. I knew prices would be higher but was unprepared for the magnitude. Apparently Oaxaca is much more on the tourist map than before and prices and availability reflect it.

While my requirements appear to be more modest than yours, one thing I noticed in my search may apply. Some places had jumps in prices beginning December 18th, obviously 1 week before Christmas. So I booked one until the 17th, then another for the duration of my stay that didn’t adjust so much upward over the holiday or beyond during high season. It was still significantly more than what I was expecting due to my lateness in booking and faulty expectations. But I’ve been so relieved since booking and in the area of the city I was hoping for I’ve accepted it and am happy with my choices.

I, too, was not prepared to abandon my plan so my advice to you would be to finely tune your search with regard to dates and even locations (I’ll be heading to the beach for 10 days with NO possibilities in Oaxaca over Day of the Dead) and use websites you may not have considered using. I found that booking.com, my usual go-to site, had little to offer and Airbnb which I also use from time to time had what I wanted with some juggling of dates. I know exactly how you’re feeling and my advice would be to consider places to stay you otherwise wouldn’t. It may open up a whole new way of doings things for you, or maybe just solve the problem of the moment. I wish you well!

I took a trip to Morelia, Patzcuaro and San Miguel a few years ago and would highly recommend. I would not miss Patzcuaro; that area is among the places in Mexico (and I've been to a LOT of places in that country) that I found most interesting. There is no advisory and even if there was, I'm pretty certain the town and surroundings are safe for travelers.
And do not miss Santa Clara del Cobre. There are hotels and inns way under that price you mentioned. I paid under $100 at a guest house a few years back.

Never been to Mexico, too and I would love to follow this thread.

Julia, Welcome to Fodor's forums. Mexico is such a huge diverse country. So many possibilities. From the colonial cities in the mountains, to huge cities like Mexico City and Guadalajara, to the beach and resort towns like Mazatlan, Acapulco, Playa del Carmen, Puerto Vallarta, Cabo San Lucas. I encourage you to pick up a couple hard-copy guidebooks (even olders ones are OK for the maps and history, I just donated some to Goodwill recently), then use the internet for current information on places to stay, transportation, etc. once you know what region of the country you are headed to, what airport you'll be using. If you rent a car or go with public transportation. I wouldn't plan a trip around them, but there are lots of entertaining travel blogs and videos you can watch, webcams showing real time views of various places...
bienvenidos/welcome