Hey Nat,
Welcome to the wonderful world of contract cleaning!
I suggest that you do re-visit the site, as it is impossible at this stage to furnish a quote.
The attitude of the person who showed you round is an all too familiar story, peoples knowledge of professional cleaning, even within the trade is not what it should be.
In my opinion, there is a very real possibility of you being led along the garden path here.
Did you ask why thier current cleaning staff are not transfering to the new office?
The implied threat of just getting a cleaner from the job centre if your price is not to his liking, is in my opinion a warning sign that you should heed. The person who showed you round this time clearly has no idea that if they employ a cleaner direct they will have to consider the following, just to name a few:
1. Health & Safety Training relevant to the cleaners job.
2. Coshh.
3. Equipment and maintenance costs.
4. Consumable purchase and control.
5. Cleaning related Risk Assessments.
6. Method Statements.
7. Holiday/Sickness cover for the cleaner.
The list does go on and on!
Regarding parking, does the site not have its own parking area?
If not, are the staff getting thier parking costs covered by the company, if so couldnt you?
Regarding storage, most insurance companies that I am aware of, will insist on your chemicals at the very least being in a locked cupboard. Chemicals left in a kitchen, some of them flammable, not a good idea! If there really is no storage, I would advise you bring them with you and take them away at the end of each shift, use triggers, dont go lugging 5ltr containers round

Your charge of £15:00 petrol, is this per week/month, trust me you wont get it, keep a record of your milage, and claim it as an expense through the business, same for servicing etc.
I also advise you to look at another post "HOW LONG" before you fix your prices, the potential client says he wants 2 hours per day 3 days a week, however this may not be sufficient to keep the building clean, you need to find the answers to the questions, before submitting your price, not find out you goofed up a month in!
When you do submit your quote, ensure that you offer them 2 prices, one for 2 hours per day, 3 days a week and another to keep the building clean properly, make sure that this is in writing and contained within your quotation, that way if 2 hours are not enough, you refer him to the quote, and say in my professional opinion in order to clean the building to a high standard it need to be cleaned x amount of hours over x amount of days.
Remember also that the building will take longer to clean each visit as twice per week you will have 2 days worth of grime to clean.
As I mentioned above, you may have to be careful when submitting your quote exactly what you put in there, too much detail, and you will enable him to employ that cleaner from the job centre, too little detail and your quote ends up "filed"
Me personally, I would see if he has undergone a change in attitude when you visit next, sit down and explain how you can solve his cleaning problems, and make a judgement, if you feel his attitude is not going to change, its a fair bet that his expectations of what can be achieved in 2 hours x 3 days is going to be impossible to meet.
Regards,
Rob