What are my options for returning to Thailand after leaving on a Student Visa without a re-entry permit?

At the least, I'd get a single entry tourist visa before you fly back here. That will stamp you in for 60 days when you get here and you could extend it for another 30 days at the immigration office for 1900baht.

You're going to need time to have your school get you NEW paperwork from the Ministry of Education (if they even can) and then go get a NEW 90day single entry Non-ED visa

Did you inform your school that you had to leave right after you came into the country on your ED visa? Most schools have rules that say as SOON as you get the ED visa from a thai consulate you go back to the school and let them get copies of your passport so they can start your paperwork for your up coming extensions.

How long are you in the UK for? Do you have enough time to get a hold of your school, have them get NEW paperwork and then send it to you so you can get a new 90 day single entry Non-ED visa BEFORE you come back?

UK passport holder is eligible for visa exempt entry.

But be aware you might need to have onward travel ticket at checking in to airline on the way back to Thailand, if you are not able to get any visa during your stay there.

It doesn't matter if Your ticket is return travel of round-trip from Thailand, airline would just check if have only one flight to go and if you have visa.

If you can get the documents from your school send to you, you can apply for a new ED visa in the UK, or apply for a Single or Multiple Entry Tourist Visa in the UK before you make your way back into Thailand.

You could have bought a re-entry permit at the airport before leaving.

If you had the Single Entry Non Immigrant ED visa, entered Thailand, left without a re-entry permit, you have to start all over again. Get the documents from the school and apply for a new ED visa, be aware that only in Vientiane Laos you can only get 1 ED visa a year.