The reason companies will not employ you if they think you're over qualified is because they know you won't be in it for the long haul, they realise it's probably just a stop gap for you until you find something better. They don't want to have to go through the whole process of hiring someone again when you eventually move on, so they look for someone who they think will stay put for a while.
If you really want to work somewhere like Greggs as a long term career then I would advise maybe removing some qualifications/experience from your CV, and in the interview really lay it on think about how you're looking for a long term career in bakeries.
Nail, meet head.
It costs money to hire, even if they don't use and agency (and most do), if they do then the agency gets about 20% of your year one salary upfront.
Then training, setting you up on the payroll, contracts, legal etc...
I got turned down for a job testing games once, I was on £50k previously (2005) but bored, went for this job seeing it as a way into a better industry, on £16k. They said "you won't fit in", mainly as the rest of the QA team were anti social 17 year olds.
It was for the best as it wouldn't have led anywhere, but at the time it was like "what the fuck???".