Your definatly NOT a subby so when it comes to doing your tax for the year the Inland Revenue will go chasing the other guy for your tax and national insurance payments.
To be a sub-contractor you MUST have some of your own clients, use your own equipment and tools, your own insurances, business bank account and detailed invoices to the other party.
Some of this can be bypassed if you "hire" your equipment, i.e van, from the other company but that is a real minefield with the taxman.
Have a chat with the local employment officer to make doubly sure or else BOTH of you could end up in trouble with the taxman.....
Regards
Mr H