The former Foxwood school is now the East Leeds Family Learning Centre, a community outpost for a consortium of colleges.
Mr Hudson, aged 45 and unemployed, has returned to learn some basic maths, English and employability skills.
"It was terrible coming back through those doors," he admits. "I hated this place as a school. That's why I needed key skills."
But now he is glad he returned. A mile away, a vast new Tesco supermarket and shopping centre is being built - Terry Hudson has the guarantee of a new job there when it opens in October.
It will be the first time he has worked in years. The job offer was there as an incentive for him to pass through basic skills and employability training.
After coming to the learning centre for several months, Terry and fellow students sailed through their job interviews.
"We were expecting it to be difficult but because they had trained us up to a higher standard, we found it easy," he says.
This scheme is being run by a partnership of Tesco and the Basic Skills Agency in areas where the supermarket chain has new stores opening.
The new Seacroft Green Shopping Centre is being heralded as a big step in the regeneration of Seacroft, a sprawling inner-city area of Leeds.
Seacroft is one of Europe's biggest housing estates. With the closure of large local employers such as Vickers, the area has been hit by unemployment.
Tesco has promised 600 jobs, mainly for local people. And in the run-up to the new development opening, the company has prepared the ground carefully.
Cynics might argue that this is all good PR - a glossy newsletter the Seacroft Partnership News promises "a new beginning for everyone in Seacroft" and to make it "a better place to live and work".
But as well as winning over the locals, Tesco has also developed a strategy of identifying the needs of the communities which will provide their shoppers and their workforce.
One of the big needs identified in Seacroft was basic skills, so the supermarket giant forged links with the East Leeds Family Learnig Centre.
"We are under no illusions," says Tesco spokeswoman Fiona Guy. "At the end of the day it is about profit. But we are getting the support of the local community, we are getting a well-trained workforce and helping to regenerate the area."
The learning centre is run by a partnership of four FE colleges - Thomas Danby College, Leeds College of Art amp; Design, Leeds College of Technology and Leeds College of Music - and Leeds Metropolitan University.
More than 50 people have been taking the Tesco training course at the centre. Of those, 42 now have a job with the firm as long as they complete the training.
Further support is offered to most of the remaining eight to give them another chance. And there is continued training avail-able for those going on to work at the store.
Richard Maitland, a tutor at the learning centre, says the standard interview for Tesco - called Select the Best - can be tough, especially for someone who may have been out of work for a while.
He said that while job offers were proving a good incentive, the training also boosted confidence.
"At the outset the training was about getting people through the interviews," he says.
"From that we identified that some people needed help. Some just wanted help with interview techniques. Others wanted help with basic English and maths."
He said this approach of offering training with the incentive of jobs at the end of it has now drawn interest from other big potential local employers.
Similar schemes are being piloted where new superstores are to be built in Preston and Litherland on Merseyside. One of the partners on Merseyside is Hugh Baird College, which will host the basic skills courses.
Alan Wells, director of the Basic Skills Agency, says: "The Tesco model will be successful because it links improving literacy and numeracy with getting a job.
"So few companies provide similar training programmes. In my view all companies moving into an area should. It's about local jobs for local people, and local basic skills training to help local people get and keep the job. That's how we'll make the radical difference we need to make."