Probably yes, you're making mistake! You shouldn't leave UK without Z visa!

I'm guessing, your Co. is not authorized to hire Foreign teachers, and cannot sponsor Z.

Once, you're in China, they'll get you business visa (F ), but it is illegal to work and receive salary in China with other visa than Z. Business visa used to be called F, and I'm not sure what is correct letter now.

If you'll find another School, which will be able to sponsor Z visa, you'll be required to return to UK, and apply for Z in Chinese Embassy in London. 

Rarely, your new School will be 'powerful' enough to apply for Z in Hong Kong.

Never mind for 'School wants ASAP'! You're required by Chinese law to exit China, when apply for Z visa. Right School should send all required docs. to Chinese Embassy in UK, which should grant you Z, and only then you should enter China.

Web link of Chinese Schools, authorized to hire FT, and sponsor Z:

http://www.anesl.com/schools/info.asp?province=Guangdong&keyword=University&cmd=Search 

Change Province, and the level of School, and enter the name of the School. Link is from 2012, and might be a bit out dated.

Thanks guys! The school is called CTP Changzhi School. It isn't on the list. :(

However, I am not entirely sure but I think the school may be new, or it may be listed under another name. I am a bit worried now though, if they aren't authorised to hire foreign workers what does this mean and why would they employ me?

I edited the Q. The name of the school is CTP Changzhi School, Changzhi, Shanxi province.

I got the impression the school might be new or something? I don't have a lot of information about it, since I'm mostly dealing with the person from TEFL panda who is acting as my recruiter. But, I did sign a contract with the school already!

if the school wants you out there as soon as possible, tell them you will be as soon as they provide the correct documents for a 'Z' visa.

if the recruiter tries to BS you, just refuse, as they are clearly not legit.

no job here in China is worth being illegal for, no matter what they promise, because you can be sure they will ***** you over

EDIT
if you are in the UK at the moment, send your recruited a clear and unambiguous email. They should get back to you by the time you are awake tomorrow (GMT)

Fully agree with the other responses. IF you do come out here and they actually do process the paperwork to get a Z visa you then have to go back to your home country to apply for the Z visa as you can't do it in Hong Kong anymore.

Who is going to pay of that return flight?
TBH they are bullshitting you. Once you get here on the tourist visa they will not make you legal...more than likely get you a dodgy business visa and then you'll need to do visa runs every 30 or 60 days.

Okay - I got a response from my recruiter.

She said that a regular work visa in China requires two years work experience and a TEFL qualification (I am still working on getting my TEFL right now). So I am not eligible for that, since I am still working on getting my TEFL. Is this true?

She mentioned that a business visa rather than a work visa might be another option? I'm kind of confused now really.

Thanks everyone for the responses. Very disapointing to me! But I appreciate the advice.

Now recruiter has offered me contact details of British person working without a working visa for several years. So I guess that means I was never going to get a working visa, which they never actually made very clear to me at all. Very sceptical now of this.

Tefl Panda,   Grace is it there ......................................run a mile from this outfit and any that dont give you documents to process (z) visa at home, and then come to China on (z)

if you come to China on (l or f) visa, you will have to fly home to the UK to process, and who do you think pays for that  flight and the other little expenses

do yourself a favour (finish your tefl),  Chinese Government dont care  how many hours your tefl is (20,40,60 or more hours is all the same to them)

whats important is you have one.

save your self so much misery by waiting until a proper school do the bizo

plus they will bend you over every chance they get,  you need to have the protection of the z visa (that way when they do try to fxxx you , you can go to PSB

Simple, what they are asking you to do is illegal. If anything goes wrong, you are screwed. Find another school and do it legally. 

Right TEFL Panda, from what I know about them, is they are a third even fourth party. They reel you in and then pass you to a local Agency. They 'hire' you but you actually sign a contract with someone completely different i.e. you will never meet the Panda people. He/She is relaying information from the particular Agency he/she wants to get you in with. They no doubt take some commission - whether a sign on fee or part of your monthly. 

I'm not saying there's anything particularly bad about them but the whole thing reeks of sneakiness imo. Sometimes/probably all the time they will not know what exact school will hire you. It is the school that gets you the Z Visa. So therefore the Agency can only offer a Business Visa at the most. You'll go to HK and apply for a Z Visa later when your school is onboard. It just takes first of all risk away for the Agency, BUT you do have the power to walk away, as any contract that will be signed, with say Business Visa, is null and void, power to you. Also you will pay for flights, medical and other sundries when they haven't paid for anything. There will not be any Chinese lessons on offer. The agency will change your CV for you - to lie to the PSB that you have the required experience - without the blink of an eye. This is after you secure the job and the kids/teachers/school like you. Risk aversion or management. Everything will be in their favour - always. Read your contract carefully - ask as many questions as you can muster up. Judge them then maybe.