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Unless you already had an Openreach white modem, you should have been sent a Smarthub which is a VDSL modem router combined.
Your Homehub 4 will not work with Infinity on its own.
You will need to contact BT and have them send out a Smarthub which is also known as the Homehub 6. Until you get one your broadband will not work.
Do not buy anything. You should have been offered one free of charge. It is part of the package you ordered. Contact BT and tell them you do not have a compatible modem/router and you need one sent out. If the refuse tell them you want to cancel your order.
The Tp Link TD-W9970 is readily available locally for less than £35. Its a combined modem/router, so you do not need to use the home hub 4.
There is an oinline review on this page.
This is the manufacturers page http://uk.tp-link.com/products/details/cat-15_TD-W9970.html
As you had already suggested to the OP to buy something it was obvious what you were refering to so it was not really necessary to point that out to me when I was informing him not to buy anything because he should have been supplied with the correct equipment.