I've delt with TUPE during a company take over but not seen it in this setting, rather tenuous common sense straining use of law, not least because its not the cleaners only job!
Anyway, I think if it were me, I would firstly record the short comings of the current people doing the job over a couple of weeks, things not done, time spent chatting, the actual things they are not doing. Then bring in the company responsible and tell them to sort it out or you will bring in a new contractor to be responsible ( you could even get a few quotes before you bring in the company)
If things don't get better then you change to company B but be mindful when you choose company B that you are really asking them to get the staff (current or new) to do the job properly and make sure their staff work to your requirements, be this by better management or use of disciplinary procedure, no need to duck around the law.