If you take a taxi make sure they know where they are going, they will always take you to the normal Chang Wattana. Show them the new location. Make sure they drop you at the right gate or its a bit of a walk too. Make sure your landlord signs the sheet with their photo ID on it and take your rental agreement.
Id would allow a month to get all the documents, at least a month (if doing in Thailand) Its easier to get the visa before entering the Kingdom from your own country but check with the embassy in your country first. You can do this when in Thailand but you need time and will have to leave the country to get the visa, from a embassy outside of Thailand, eg Loas Vietnam.
I think Universities can process the ED Visa without you leaving if your want to do a degree course, but not a language school. You need to leave the country.
Have a look on a UK Thai consulate website its all stated on there, I think you would be ok, but best to check. Give Hull a call they normally answer the phone and are pretty helpful.