24k to 26k is low for London. If you're poor already then your standard of living might not change much.

Try using various cost of living calculators to figure out where and how far your money will have to go - I don't know where exactly in the South you come from, but I picked the two Southern states tied for median cost of living (the Carolinas) and stuck some random towns and cities into the calculator. Rent in particular is often 250% higher or more, and your local purchasing power will be in the region of 20-40% lower.

Taxes: The USA has generally lower taxes than the UK, but for the most easily comparable tax - income tax - you'll probably pay roughly the same at the 24-26k level. From what I can tell, National Insurance (UK version of Social Security) is higher UK. VAT (sales tax) is 20% on everything except life necessities (food, insurance, healthcare, childcare goods), which is over double the highest total sales tax rate (Tennessee, 9.44%). VAT is calculated into the display price of the product unlike in some US jurisdictions. These are probably all factored into the cost of living calculator above, but it's worth keeping in mind. All in all, you'll be taking home less of your salary whatever your income level. Healthcare costs are included in the above taxes though, and you'll be entitled to the same treatment as a British citizen in almost all cases.

Since you're (presumably) not a citizen of any EEA country nor a refugee, you can't claim housing benefit upon arrival. You can only get it once you have "habitual residence" status, which means you intend to stay here long-term and have been here for a (intentionally vaguely-defined) "appreciable period of time". So, upon arrival you can forget about any housing stipend unless your employer is generous - you'll have to look into shared accommodation or get really lucky. (Did that London LW house ever get started?)

For transport, your first port of call ought to be the bus network. There's a flat fare across the whole city and it's much cheaper than the tube. Annual fare for an adult is about £800. If for whatever reason you can't use the bus, the tube network is more expensive, and it will also depend on where exactly the school is in London, and where exactly you can get cheap rent. The annual fare will be in the range £1000 - £3000 for an adult, depending on the zones you're travelling to and from. Petrol prices are much higher in the UK than in the USA.

I tried doing a Fermi estimate with a bunch of different estimates of your requirements to figure out how much disposable income you'd have, but they ended up all over the map (negative £2000/year to £4000/year). You can survive, but depending on how much luxury you like to live in I can't say if you'll thrive.

What's the job market for teachers like in your home state, or the US as a whole? If prestigious British schools are willing to take you on, why not American ones?