Armourtex were very good at media blasting once they got the hang of it. They also gathered a lot of bike specific knowledge (through trial and error) which meant you could trust that they wouldn't strip any threads or ruin any finishes. That used to run at £40 or thereabouts depending on how nicely you asked and who you were.
Industrial places that do powder coating on tractors and fridges are good bet for a cheap blast. In the region of £15 just off the OKR but no bike specific knowledge so you have to bung all your threads yourself to avoid them being rekt.
At Cole Coatings Workshop, all carbon is backed off by hand using abrasives at various grades. All stainless and similar is done by hand using an industry standard stripper called "starchem". If this is the route you want to take and your time is valuable, use starchem, some wellies and a jet washer.
Our media blasting is done in West London by a private firm in batches. If you wanted to get your frame to us, we could pool it in with ours. Can take a week to ten days for return.
If you're after super crisp stuff rather than simple paint removal, the guys at Enigma are the best. You can choose the blast medium and grain size and stuff.
Cheapest way is to strip it by hand though. Then obviously if it's steel, it will need to be keyed and primed quickly.
Feel free to DM me if you have any questions.