Some good tips from the PP.
I would add that ideally you need to get a project team together which includes either a member or backing from senior management and two people from the shop floor; one who you think will be easy to convince, another who is one of the most vocal opponents, however, is someone who is obviously intellegent.
Then I would tie in your clean as you go into a general food safety, efficiency or health and safety drive (after all you can approach it from many different directions.) For example, you could look at 5S or slips trips and falls.
Explain your aim to this team, i.e. you want the factory to have improved standards of daily cleanliness (if that is the aim) or you want to remove slip hazards. Then get them to come up with solutions. Set some constraints, e.g. We can spend £200 on equipment but there is no additional funding for extra staff.
It will depend a lot on you, the management and the culture of your site as to whether something like that works but even if it doesn't, I don't think it would be a wasted exercise. You've treated everyone as adults and tried to involve them. If they then reject that, there is no real cause for them to complain if a solution gets imposed on them to some degree but then once you've opened that door saying "I want to involve you in the solutions" you might find the next problem that comes up, they might see the point and work with you.
I suggest using someone who is very vocal because there are such things in teams as "cultural architects" and "negative terrorists". I don't mean the latter in a literal way btw. What I mean by this is that these people are the vocal people in a team who are listened to by their peers. If you involve these people and get them on board, they will bring the team with them. If you exclude them, they can become disaffected and bring everyone else down. Therefore you don't always need to convince everyone, you need to convince the key influential people and the others will follow. 