The cash was stolen from the Sunwin Services Group (SSG) premises in Broxburn with the thieves understood to have used keys and pass codes to carry out the raid.
An investigation is now under way into the security breach at the facility which holds money for the Co-operative Group's cash machines.
Police today appealed for any witnesses to come forward as inquiries into the theft, which happened between 8pm and 10pm on Friday night, continued.
The depot is based on Freskyn Place at the East Mains Industrial Estate and is known to have tight security. Police are now investigating how the thieves were able to lay their hands on the keys and codes.
Workers from R&J Strang at a nearby unit on the industrial estate were shocked after hearing about the robbery.
Declan Henderson was working on Friday night at around the time of the heist. He said: "We supply the tyres for their trucks and our guys are in there all the time.
"Security is very tight and you can't walk anywhere in there without being on camera so whoever done it must have known this and how to sort that out.
"There is usually activity there until about 10pm and I think there's usually engineers there all the time for call-outs in case they need to fix the ATMs, but you never see any vans at that time of night."
He added: "I received a phone call from head office on Sunday asking if our CCTV cameras were operational but they aren't, then I saw some CID officers at the building who paid me a bit of attention when I passed.
"We're a 24-hour service and someone is here all the time but no-one has even questioned us about it."
Another worker said: "We've all been inside and there are two security doors that operate separately so you can't get in or out without the other one.
"They probably wouldn't have even needed to use to a van or anything because you could probably fit a quarter of a million into a suitcase if it was in bank notes for ATMs. It's a bit of a shock to hear what's happened and how much money is involved."
A police spokesman said today an investigation was ongoing.
"Police are investigating the theft of a six-figure sum of money from a business premises in Broxburn.
"The theft happened sometime between 8pm and 10pm on Friday.
"Inquiries are ongoing and anyone with any information should contact the police immediately."
Based in Bradford, SSG operates a number of security depots across the UK, collecting and delivering cash for customers, as well as paperwork and company documents.
The company has accredited status with the Security Industry Authority's contractor scheme.
The Security Industry Authority ensures that security businesses employ trained staff who have been fully vetted.
SSG also has a team of engineers responsible for maintenance of ATM machines across the country.
No-one from SSG could be reached for comment.